Open problems in topology. (Q1421986)

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scientific article; zbMATH DE number 2037246

Language	Label	Description	Also known as
English	Open problems in topology.	scientific article; zbMATH DE number 2037246

Statements

scholarly article

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Open problems in topology. (English)

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Topology and its Applications

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publication date

3 February 2004

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MaRDI profile type

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Essential cohomology of finite groups

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On Banach-Mazur compacta

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Embedding of compacta, stable homotopy groups of spheres, and singularity theory

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Generalized Daverman's problem

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West’s problem on equivariant hyperspaces and Banach-Mazur compacta

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Function Spaces of Completely Metrizable Spaces

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\(K\)-theoretic groups with positioning map and equivariant surgery

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Limits in the uniform ultrafilters

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On Collectionwise Normality of Locally Compact, Normal Spaces

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A small Dowker space in ZFC

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A normal screenable nonparacompact space in ZFC

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Dowker spaces and paracompactness questions

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Nonshrinking open covers and K. Morita's duality conjectures

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On a problem of C. H. Dowker

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Characterization of spaces admitting a homotopy dense embedding into a Hilbert manifold

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Toward a topological classification of convex sets in infinite-dimensional Fréchet spaces

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Universalité forte pour les sous-ensembles totalement bornés. Applications aux espaces $C_{p}(X)$

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Interplay between strongly universal spaces and pairs

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Characterizations of \((\mathbb{R}^{\infty}, \sigma)\)- or \((Q^{\infty}, \Sigma)\)-manifolds and their applications

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On disjoint Borel uniformizations

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On absolute retracts of ω*

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The dynamics of the Hénon map

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A metric space of A. H. Stone and an example concerning 𝜎-minimal bases

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On the set of points with a dense orbit

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Affine and homeomorphic embeddings into $\ell ^2$

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Admissibility, homeomorphism extension and the AR-property in topological linear spaces

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The order type of the set of Pisot numbers

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The almost-disjointness number may have countable cofinality

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Mutually complementary partial orders

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Partial order complementation graphs

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The number of complements of a topology on \(n\) points is at least \(2^ n\) (except for some special cases)

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Topology of homology manifolds

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Topology of homology manifolds

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One fixed point actions on low-dimensional spheres

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A note on iterated duals of certain topological spaces

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Indépendance linéaire et classification topologique des espaces normés

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Un espace métrique linéaire qui n'est pas un rétracte absolu

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Une caractérisation des rétractes absolus de voisinage

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Un exemple de sous-groupe additif de l'espace de Hilbert

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Solution to the Schauder fixed point problem

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Applying Coordinate Products to the Topological Identification of Normed Spaces

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On a question of de Groot and Nishiura

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Weak neighborhoods and Michael-Nagami's question

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Compact-covering maps and $k$-networks

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On \(UV^ n\)-equivalent compacta

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Cohomological dimension of Tychonov spaces

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On the non-productivity of normality in Moore spaces

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Crowded rational ultrafilters

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A CONJECTURE OF KAUFFMAN ON AMPHICHEIRAL ALTERNATING KNOTS

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PL Maps with Manifold Fibers

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Controls on the plus construction

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Crumpled laminations and manifolds of nonfinite type

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Selections Boreliennes Injectives

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Compact covering and game determinacy

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Compact-covering-properties of finite-to-one mappings

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Two point set extensions- a counterexample

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ON SETS THAT MEET EVERY HYPERPLANE IN <i>n</i>-SPACE IN AT MOST <i>n</i> POINTS

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A solution to van Douwen's problem on Bohr topologies

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Extending Homeomorphisms and Applications to Metric Linear Spaces Without Completeness

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Failure of the Factor Theorem for Borel pre-Hilbert spaces

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Narrow coverings of \(\omega\)-ary product spaces

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Star covering properties

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More set-theory for topologists

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On the character of normal non-CWH spaces

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Two results on special points

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Remarks on Partitioner Algebras

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On Closed Subspaces of ω ∗

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Cut Points in Cech-Stone Remainders

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A new subcontinuum of 𝛽ℝ\ℝ

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Homogeneity in powers of zero-dimensional first-countable spaces

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Not all σ-Complete Boolean Algebras are Quotients of Complete Boolean Algebras

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Two real ultrafilters on \(\omega\)

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A fibration that does not accept two disjoint many-valued sections

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On the Failure of the Urysohn-Menger Sum Formula for Cohomological Dimension

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Light maps and extensional dimension

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Span and plane separating continua

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A New Finite Loop Space at the Prime Two

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Union Theorem for Cohomological Dimension: A Simple Counterexample

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Cohomological dimension and metrizable spaces. II

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Universal Cell-Like Maps

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Function spaces and shape theories

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Spaces Without Cohomological Dimension Preserving Compactifications

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Infinite dimensional compacta having cohomological dimension two: An application of the Sullivan conjecture

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CH and first countable, countably compact spaces

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Gently killing \(S\)-spaces

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CH with no Ostaszewski spaces

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Dimension phenomena associated with \(\beta \mathbb N\)-spaces

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A Moore space with a 𝜎-discrete 𝜋-base which cannot be densely embedded in any Moore space with the Baire property

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Killing normality with a Cohen real

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Countably compact groups from a selective ultrafilter

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Mal'tsev and retral spaces

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Homotopically non-trivial additive subgroups of Hilbert spaces

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Spaces in Which the Nondegenerate Connected Sets Are the Cofinite Sets

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Forcing and normality

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Some compact contractible manifolds containing disjoint spines

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Open mappings looking like projections

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Continuous selections and \(C\)-spaces

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Detecting codimension one manifold factors with the disjoint homotopies property

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Every lattice with 1 and 0 is embeddable in the lattice of topologies of some set by an embedding which preserves the 1 and 0

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On the regularity of homeomorphisms of \(E^n\)

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Borsuk's index and pointed movability for projective movable continua

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Ganea's Conjecture on Lusternik-Schnirelmann Category

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A\(_{\infty}\)-method in Lusternik-Schnirelmann category

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The converse to the fixed point theorem of P. A. Smith. I

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On countably compact, locally countable spaces

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More countably compact, locally countable spaces

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Convergent Free Sequences in Compact Spaces

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A counterexample to Borsuk’s conjecture

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Ideals on \(\omega\) which are obtained from Hausdorff-gaps

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A noncontractible cell-like compactum whose suspension is contractible

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The nonexistence of expansive homeomorphisms of Peano continua in the plane

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Embeddability into the plane and movability on inverse limits of graphs whose shift maps are expansive

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Refinable maps in the theory of shape

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On local 1-connectedness of Whitney continua

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The nonexistence of expansive homeomorphisms of a class of continua which contains all decomposable circle-like continua

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On the map theorem

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Reformulating the map color theorem

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Collectionwise Hausdorffness at limit cardinals

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A conjecture of Barratt-Jones-Mahowald concerning framed manifolds having Kervaire invariant one

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A ZFC Dowker space in ℵ_{𝜔+1}: An application of pcf theory to topology

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On the Complete Invariance Property in Some Uncountable Products

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A Lindelöf space with no Lindelöf subspace of size $\aleph \textunderscore 1$

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At most 4 topologies can arise from iterating the de Groot dual

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Finitely Cyclic Homogeneous Continua

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A Two-Point Set Must be Zero-Dimensional

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Rim-finite, arc-free subsets of the plane

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Bohr topologies and partition theorems for vector spaces

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Reflection and Weakly Collectionwise Hausdorff Spaces

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Locally compact perfectly normal spaces may all be paracompact

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Failure of normality in the box product of uncountably many real lines

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Homogeneity in powers of subspaces of the real line

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When does the class \([{\mathcal A} \longrightarrow {\mathcal B}]\) consist of continuous domains?

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On linear continuous open surjections of the spaces \(C_ p(X)\)

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The Free Abelian Topological Group and the Free Locally Convex Space on the Unit Interval

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Certain finite dimensional maps and their application to hyperspaces

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A generalization of Kelley’s theorem for 𝐶-spaces

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The space of subcontinua of a 2-dimensional continuum is infinite dimensional

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Continuous \(L\)-domains

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The first homotopy group of a finite \(H\)-space

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mod 3 cohomology algebras of finite \(H\)-spaces

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Solutions to two problems of J. D. Lawson and M. Mislove

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On topological embeddings of linear metric spaces

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On Sets which Meet each Line in Exactly Two Points

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Open problems in topology

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Open problems in topology

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Open problems in topology

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Open problems in topology

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Open problems in topology

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Open problems in topology

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An Atriodic Simple-4-OD-Like Continuum Which is Not Simple-Triod-Like

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A Periodic Point Free Homeomorphism of a Tree-Like Continuum

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A hereditarily indecomposable tree-like continuum without the fixed point property

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About a problem of Ulam concerning flat sections of manifolds

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Some of the combinatorics related to Michael’s problem

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On one fixed point actions on spheres

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Most standard spheres have smooth one fixed point actions of \(A_ 5\). II

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Tree-like continua do not admit expansive homeomorphisms

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Small inductive dimension of completions of metric spaces

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Small inductive dimension of completions of metric spaces. II

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CE-Equivalence, UV k -Equivalence and Dimension of Compacta

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The Compact Neighborhood Extension Property and Local Equi-Connectedness

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The AR-property for Roberts’ example of a compact convex set with no extreme points Part 2: Application to the example

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Fixed point sets and tangent bundles of actions on disks and Euclidean spaces

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Universal spaces in the theory of transfinite dimension, I

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Exponents and the cohomology of finite groups

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Corrections to: Fixed point sets of smooth group actions on disks and Euclidean spaces

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Open problems in topology, seventh status report

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On metrizable <i>E</i> with <i>C</i> <sub> <i>p</i> </sub> ( <i>E</i> ) ≇ <i>C</i> <sub> <i>p</i> </sub> ( <i>E</i> ) × <i>C</i> <sub> <i>p</i> </sub> ( <i>E</i> )

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A homogeneous arcwise connected non-locally-connected curve

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Martin's Axiom does not imply perfectly normal non-archimedean spaces are metrizable

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Topological density of ccc Boolean algebras–Every cardinality occurs

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Absorbing spaces for \(C\)-compacta

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Homogeneous products of spaces

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An answer to A.D.Wallace’s question about countably compact cancellative semigroups

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Higher dimensional aposyndetic decompositions

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Characterizing cohomological dimension: The cohomological dimension of \(A \cup{} B\)

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Collectionwise Normality in Screenable Spaces

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A Cyclic Monotonically Normal Space which is not K 0

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A Cellular Wedge in R 3

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The Cohomology of the Groups of Order 32

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An alternative proof of Cauty-Geoghegan's characterization of ANRs

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Disjoint spine phenomena in certain contractible \(n\)-manifolds (\(n\geq 5\))

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Counterexample to a problem of Geoghegan-West

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Imbeddings into topological groups preserving dimensions

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A compact Hausdorff topology that is a T<sub>1</sub>-complement of itself

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CON(\(\mathfrak u>\mathfrak i\))

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The distributivity numbers of $\mathcal {P}(\omega )$/fin and its square

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PFA Implies all Automorphisms are Trivial

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Somewhere Trivial Autohomeomorphisms

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Martin's axiom is consistent with the existence of nowhere trivial automorphisms

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Extensions of perfect GO-spaces and $\sigma $-discrete dense sets

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A non-metrizable compact linearly ordered topological space, every subspace of which has a 𝜎-minimal base

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First countable extensions of regular spaces

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Paranormal spaces under $\diamondsuit ^{*}$

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Lindelöf property and the iterated continuous function spaces

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The space of composants of an indecomposable continuum

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Some results on gaps

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Martin's axiom and the transitivity of \(P_{\mathfrak c}\)-points

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<i>N</i> <sup>∗</sup> does not Contain an Algebraic and Topological Copy of β<i>N</i>

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σ-Centred Forcing and Reflection of (Sub)Metrizability

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Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

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No submaximal topology on a countable set is $\mathbf {T}_{\mathbf {1}}$-complementary

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Partition Problems in Topology

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Calibres of first countable spaces

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The Wallace Problem: A Counterexample from Ma<sub>Countable</sub>and<sub>p</sub>-Compactness

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A group under \(\text{MA}_{\text{countable}}\) whose square is countably compact but whose cube is not

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Two Moore manifolds

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Every Uncountable Abelian Group Admits a Nonnormal Group Topology

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On finite-dimensional maps II

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The epimorphism problem for Hausdorff topological groups

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A note on a question of R. Pol concerning light maps

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Concerning the spans of certain plane separating continua

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Group actions and group extensions

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A space with infinite span and zero surjective span

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Universal map of \(\sigma\) onto \(\Sigma\) and absorbing sets in the classes of absolute Borelian and projective finite-dimensional spaces

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Absorbing sets for<i>n</i>-dimensional spaces in absolute Borel and projective classes

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Absorbing sets in the Hilbert cube related to cohomological dimension

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On periodic compact groups

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full work available at URL

https://doi.org/10.1016/s0166-8641(03)00183-4

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Identifiers

zbMATH Open document ID

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10.1016/S0166-8641(03)00183-4

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Mathematics Subject Classification ID

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zbMATH DE Number

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Sitelinks

Mathematics(1 entry)

mardi Publication:1421986

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