Some aspects of dimension theory for topological groups

DOI10.1016/j.indag.2016.11.024zbMath1385.54011OpenAlexW2766471875MaRDI QIDQ1688957

Alexander V. Arhangel'skii, Jan van Mill

Publication date: 12 January 2018

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.indag.2016.11.024

zbMATH Keywords

topological grouphomogeneous spaceBrouwerdimension theoryhomeomorphism group

Mathematics Subject Classification ID

Topological groups (topological aspects) (54H11) Dimension theory in general topology (54F45)

Related Items (3)

A solution to a problem about the Erdős space ⋮ Editorial: Alexander Vladimirovich Arhangel'skii ⋮ The impact of Pontryagin and Bohr functors on large-scale properties of locally compact abelian groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Compact homeomorphism groups are profinite
• Topological groups with a \(bc\)-base
• A complete classification of homogeneous plane continua
• Flat spaces for which the Jordan curve theorem holds true
• Über eine Verallgemeinerung des Jordanschen Kurvensatzes auf zweifach geordnete Mengen
• Imbeddings into topological groups preserving dimensions
• Topological groups and related structures
• Covering dimension of topological products
• Nonequality of dimensions for metric groups
• A universal topological group with countable base
• Spaces \(N\cup\mathcal R\) and their dimensions
• Separable complete ANR's admitting a group structure are Hilbert manifolds
• Spaces which do not embed in topological groups of the same dimension
• The homeomorphism group of a compact Hilbert cube manifold is an ANR
• A problem of coincidence of dimensions in topological groups
• A comparative survey of selected results and open problems concerning topological groups, fields and vector spaces
• Quotients of zero-dimensional precompact abelian groups
• Compactness and connectedness in topological groups
• More examples of metric spaces where the inductive dimensions disagree
• Transitive actions of compact groups and topological dimension
• Transformation groups and \(C^ *\)-algebras
• A homogeneous indecomposable plane continuum
• Concerning hereditarily indecomposable continua
• On the conjecture of Iwasawa and Gleason
• A generalization of a theorem of Gleason
• Normal families and dimension theory for metric spaces
• A topology for spaces of transformations
• Neuaufbau der Endentheorie
• Pseudo-Arcs and Connectedness in Homeomorphism Groups
• Erdos space and homeomorphism groups of manifolds
• A note on embeddings manifolds into topological groups preserving dimensions
• The dimension of products of complete separable metric spaces
• Note on dimension theory
• Another Homogeneous Plane Continuum
• On imbedding a metric space in a product of one-dimensional spaces
• On the dimension of compact spaces
• Resolving a question of Arkhangel'skiĭ's
• Topological homogeneity. Topological groups and their continuous images
• Classes of topological groups
• Dimensions of Topological Groups Containing the Bouquet of Two Circles
• On All Kinds of Homogeneous Spaces
• A Scattered Space that is not Zero-Dimensional
• Čech cohomology and covering dimension for topological spaces
• Spaces with increment of dimension n
• Addition and correction to the paper "On stability and products", Fund. Math. 93 (1976), pp. 81-95
• The dimension of product spaces
• Zero-Dimensionality of Some Pseudocompact Groups
• On the Dimension of Certain Totally Disconnected Spaces
• Small inductive dimension of completions of metric spaces
• On homeomorphism groups of Menger continua
• Complete Erdős space is unstable
• New properties of Mrowka’s space $\nu \mu _0$
• Universal Abelian topological groups
• Small inductive dimension of completions of metric spaces. II
• On Homeomorphism Groups and the Compact-Open Topology
• An Example in Dimension Theory
• Nonequality of Dimensions for Metric Spaces
• Locally Compact Full Homeomorphism Groups are Zero-Dimensional
• Using Flows to Construct Hilbert Space Factors of Function Spaces
• The Space of Homeomorphisms on a Compact Two-Manifold is an Absolute Neighborhood Retract
• A note on the dimension Dind
• A metric condition which implies dimension $\le 1$
• On a metric characterizing dimension
• On the dimension of non-separable spaces. I
• Characterizing 𝑘-dimensional universal Menger compacta
• The structure of compact groups. A primer for the student -- a handbook for the expert

This page was built for publication: Some aspects of dimension theory for topological groups