General topology (set-theoretic trend)

DOI10.1007/BF01084982zbMath0434.54001WikidataQ29038960 ScholiaQ29038960MaRDI QIDQ1139822

V. I. Malykhin, V. I. Ponomarev

Publication date: 1975

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

zbMATH Keywords

ultrafilterSouslin numberextremally disconnected spacesdiscrete spacescomplementation in lattices of topologiescotopologieshereditary density and hereditary Lindelöfnessmaximal and minimal topologiespower of topological spaces

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to general topology (54-02) Nonstandard topology (54J05)

Related Items (1)

Specification of topological spaces by algebraic systems of continuous functions

Cites Work

• A connected Hausdorff space which is not contained in a maximal connected space
• Basic intervals in the lattice of topologies
• Classes of spaces not containing dyadic bicompacta of large weight
• Exponents of some N-compact spaces
• Finite sums from sequences within cells of a partition of N
• An extension that nowhere has the Frechet property
• On square-compact cardinals
• Wann sind alle stetigen Abbildungen in \(Y\) konstant? (When are all continuous mappings in \(Y\) constant?)
• Nicht alle \(T_ 2\)-minimalen Räume sind von 2. Kategorie. (Not all \(T_ 2\)-minimal spaces are of second category)
• Fortsetzbarkeit stetiger Abbildungen und Kompaktheitsgrad topologischer Räume. (Extendability of continuous mappings and compactness degree of topological spaces)
• Normal families and completely regular spaces
• On products of maximally resolvable spaces
• E-kompakte Räume. (E-compact spaces)
• Ordinal invariants for topological spaces
• Universal homogeneous Boolean algebras
• Homeomorphisms of three subspaces of \(\beta N-N\)
• Quotients of the space of irrationals
• A co-topological application to minimal spaces
• Local compactness and Cartesian products of quotient maps and k-spaces
• Bi-quotient maps and Cartesian products of quotient maps
• Wallman and Z-compactifications
• Further results on E-compact spaces. I
• On the equivalence of normality and compactness in hyperspaces
• \(C\)-compact spaces
• Gelfand and Wallman-type compactifications
• Functionally compact and \(C\)-compact spaces and mappings of minimal Hausdorff spaces
• Non-existence of certain topological expansions
• Co-absolutes of remainders of Stone-Čech compactifications
• Katětov extension as a functor
• Some \(\aleph_ 0\)-bounded subsets of Stone-Čech compactifications
• Products of minimal Urysohn spaces
• Cardinality of k-complete Boolean algebras
• On Wallman-type, regular Wallman-type and z-compactifications
• Classifying almost-disjoint families with applications to \(\beta N-N\)
• A note on minimal topological spaces
• A normal hereditarily separable non-Lindelöf space
• Iterated Cohen extensions and Souslin's problem
• Separability properties of almost-disjoint families of sets
• Generic covers and dimension
• On N-compactness and measureability properties
• Souslin's conjecture as a problem on the real line
• Projective covers as subquotients of enlargements
• On k-spaces, k\(_R\)-spaces and k(X)
• S(a) spaces and regular Hausdorff extensions
• Wallman compactifications on E-completely regular spaces
• A problem of set-theoretic topology
• The decomposition series of a convergence space
• Universal relational systems
• On the Depth of Topological Spaces
• Ultrafilters and almost disjoint sets
• Normal Moore Spaces in the Constructible Universe
• On Countably Compact, Perfectly Normal Spaces
• A consistency result concerning hereditarily α-Lindelöf spaces
• Some results on expansions for normal and completely normal spaces.
• Bi-quotient maps, countably bi-sequential spaces and related topics
• Strongly non-blumberg spaces
• A note on [a, b-compactness]
• A Space of Small Spread Without the Usual Properties
• An Example of Two Compact Hausdorff FrÉChet Spaces Whose Product is not Frechet
• Characterizations of compactness and countable compactness
• Compactifications and Semi-Normal Spaces
• Remarks on dyadic spaces, II
• The Lattice of Topologies: Structure and Complementation
• On convergence spaces and their sequential envelopes
• Complementation in the Lattice of T 1 -Topologies
• Remarks on spaces of large cardinal number
• Products of Nearly Compact Spaces
• Spaces without Large Projective Subspaces.
• The Lattice of all Topologies is Complemented
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• Compact Spaces are Inverse Limits of Supercompact Spaces
• The Compactifications to Which an Element of C ∗ (X) Extends
• Two Examples on Preimages of Metric Spaces
• Free Topological Groups and the Projective Dimension of a Locally Compact Abelian Group
• H-closed extensions I
• Prabir Roy's space Δ is not n-compact
• Some Consequences of Martin’s Axiom and the Negation of the Continuum Hypothesis
• On expansions of a Urysohn space to a regular space.
• Maximal topologies
• The Growth of Subuniform Ultrafilters
• The Rudin-Keisler Ordering of P-Points
• Independence results concerning the number of nowhere dense sets necessary to cover the real line
• On some problems of Hausdorff and of Sierpiński
• Compact Sets of Functions and Function Rings
• On Wallman-type compactifications
• Complementation in the lattice of regular topologies
• Topologies with $T_1$-complements
• A T 1 -Complement for the Reals
• Wallman spaces and compactifications
• Maximal connected topologies
• Product Spaces for Which the Stone-Weierstrass Theorem Holds
• On the Existence of c-Points in βN\N
• Homogeneous Universal Relational Systems.
• From accessible to inaccessible cardinals (Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones)
• SOUSLIN'S PROBLEM
• On sequentially regular convergence spaces
• Cartesian products and dyadic spaces
• On H-Closed and Minimal Hausdorff Spaces
• [https://portal.mardi4nfdi.de/wiki/Publication:5566265 Products of k � -Spaces]
• Metric Spaces in which Blumberg's Theorem Holds
• A Countable Minimal Urysohn Space is Compact
• On countable multiple point compactifications
• A Note on Wallman Spaces
• The α-Closure αX of a Topological Space X
• On the Sum of Two Borel Sets
• Products with Closed Projections
• THE PRODUCT OF TOPOLOGICAL GROUPS AND EXTREMAL DISCONNECTEDNESS
• A Stone-Cech Compactification for Limit Spaces
• Existence and Uniqueness Theorems for Extensions of Zero-Dimensional Compact Metric Spaces
• A new kind of compactness for topological spaces
• Products of M-Compact Spaces
• Independence results concerning a problem of N. Lusin
• Some Strengthenings of the Ulam Nonmeasurability Condition
• Some Sufficient Conditions for Maximal-Resolvability⁽¹⁾
• Families of Mutually Complementary Topologies
• Regular-Closed, Urysohn-Closed and Completely Hausdorff-Closed Spaces
• A survey of cardinal invariants
• Wallman-Type Compactifications and Products
• Sequence-covering and countably bi-quotient mappings
• Internal cohen extensions
• Products of Weakly-ℵ-Compact Spaces
• Remarks on Baire theorem for H-closed spaces
• The Stone Space of the Saturated Boolean Algebras
• The cardinality of first countable spaces
• A Characterization of Order Topologies by Means of Minimal T 0 -Topologies
• Inverse limits and hyperspaces
• Metric spaces in which a strengthened form of Blumberg's theorem holds
• The Existence of Certain Ultrafilters on N and a Conjecture of Graham and Rothschild
• Relative Types of Points in βN - N
• On discrete subspaces of product spaces
• A note on $C$-compact spaces
• Ultrafilters on a countable set
• A Compactification of Locally Compact Spaces
• Products with Closed Projections. II
• Some Wallman Compactifications Determined by Retracts
• On the nonseparable theory of Borel and Souslin sets
• m-adic spaces
• Regular Compactifications of Convergence Spaces
• On two problems of A.V. Archangel'skiĭ
• Every lattice is embeddable in the lattice of $T_1$-topologies
• A quintuple quotient quest
• Nonstandard topology and extensions of monad systems to infinite points
• Some classes of E-Compactness
• Properties of Stone-Cech Compactifications of Discrete Spaces
• The box product of countably many compact metric spaces
• Non-separable Borel, sets, II
• Short complete nested sequences in βN⧹N and small maximal almost-disjoint families
• A REMARK ON A CERTAIN LEMMA ABOUT METRIC SPACES
• Infinitesimals
• The Sorgenfrey topology is a join of orderable topologies
• On the weight of Hausdorff spaces
• A topological characterization of products of compact totally ordered spaces
• Discrete Subsets of Perfectly Normal Spaces
• Invariant metrics on free topological groups
• Product spaces and the stone-weierstrass theorem
• The Topological Complementation Theorem a la Zorn
• Saturated Structures and a Theorem of Arhangelskii
• A Lindelöf space X such that $X^2$ is normal but not paracompact
• On a question of Arhangel'skiǐ
• On the non-separable theory of k-borel and k-souslin sets

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