Zero-Dimensionality of Some Pseudocompact Groups

DOI10.2307/2160252zbMath0846.54027OpenAlexW4244069825MaRDI QIDQ4290874

Dikran Dikranjan

Publication date: 3 October 1996

Full work available at URL: https://doi.org/10.2307/2160252

zbMATH Keywords

torsion groupconnected componenttotal disconnectednesscountably compact groupquasi-componentzero-dimensional groupconnected grouphereditarily disconnected grouptotally minimal groupzero-dimensionalityhereditarily pseudocompact grouptotally disconnected topological group

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Compactness (54D30) ``(P)-minimal and ``(P)-closed spaces (54D25) Connected and locally connected spaces (general aspects) (54D05) Dimension theory in general topology (54F45)

Related Items (22)

Countably compact groups having minimal infinite powers ⋮ Some pseudocompact-like properties in certain topological groups ⋮ Dimension and entropy in compact topological groups ⋮ CLP-compactness for topological spaces and groups ⋮ Some aspects of dimension theory for topological groups ⋮ On the quasi-component of pseudocompact abelian groups ⋮ Productivity of sequences with respect to a given weight function ⋮ On powers of countably pracompact groups ⋮ A survey on reflexivity of abelian topological groups ⋮ A pseudocompact group which is not strongly pseudocompact ⋮ Characterizing Lie groups by controlling their zero-dimensional subgroups ⋮ The impact of Pontryagin and Bohr functors on large-scale properties of locally compact abelian groups ⋮ On zero-dimensionality and the connected component of locally pseudocompact groups ⋮ Selective sequential pseudocompactness ⋮ Sequentially complete groups: Dimension and minimality ⋮ Forcing hereditarily separable compact-like group topologies on Abelian groups ⋮ Characterizing sequences for precompact group topologies ⋮ Sequential completeness of quotient groups ⋮ Quotients of zero-dimensional precompact abelian groups ⋮ Recent advances in minimal topological groups ⋮ Compactness and connectedness in topological groups ⋮ Uniform quasi components, thin spaces and compact separation

Cites Work

• Concerning connected, pseudocompact Abelian groups
• Imbeddings into topological groups preserving dimensions
• An example of a planar group whose quasicomponent does not coincide with its component
• Pseudocompactness and uniform continuity in topological groups
• Some properties of connected compact groups
• Compact-Like Totally Dense Subgroups of Compact Groups
• Pseudocompact and Countably Compact Abelian Groups: Cartesian Products and Minimality
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