Imbeddings into topological groups preserving dimensions

DOI10.1016/0166-8641(90)90008-PzbMath0709.22001MaRDI QIDQ921127

Dmitrij B. Shakhmatov

Publication date: 1990

Published in: Topology and its Applications (Search for Journal in Brave)

zbMATH Keywords

weightsdimensiontopological spacesimbeddingtopological groupsfree precompact groupTychonov space

Mathematics Subject Classification ID

Structure of general topological groups (22A05) Compact groups (22C05) Dimension theory in general topology (54F45) Embedding (54C25)

Related Items (21)

Varieties generated by countably compact Abelian groups ⋮ Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension \(\text{ind}\) ⋮ The torsion Bohr topology for Abelian groups. ⋮ Contributions to the Bohr topology by W.W. Comfort ⋮ Remarks on the Bohr-torsion topology of a locally compact abelian group ⋮ Some aspects of dimension theory for topological groups ⋮ The product of Lindelöf groups and \(\mathbb{R}\)-factorizability ⋮ Open problems in topology. ⋮ Characterizing Lie groups by controlling their zero-dimensional subgroups ⋮ Topological groups all continuous automorphisms of which are open ⋮ Dimensions of Topological Groups Containing the Bouquet of Two Circles ⋮ Zero-Dimensionality of Some Pseudocompact Groups ⋮ Spaces which do not embed in topological groups of the same dimension ⋮ The separable quotient problem for topological groups ⋮ A note on embeddings manifolds into topological groups preserving dimensions ⋮ A problem of coincidence of dimensions in topological groups ⋮ Selectively pseudocompact groups without infinite separable pseudocompact subsets ⋮ A comparative survey of selected results and open problems concerning topological groups, fields and vector spaces ⋮ Quotients of zero-dimensional precompact abelian groups ⋮ The dimension of an LCA group in its Bohr topology ⋮ Compactness and connectedness in topological groups

Cites Work

• On covering dimension and inverse limits of compact spaces
• On the non-existence of elements of Hopf invariant one
• Closed embeddings into pseudocompact spaces preserving the covering dimension
• Uniform free topological groups and Samuel compactifications
• A problem of coincidence of dimensions in topological groups
• Beweis des Mengerschen Einbettungssatzes
• Homotopy invariant algebraic structures on topological spaces
• Factorization of mappings of topological spaces and homomorphisms of topological groups in accordance with weight and dimension \(\text{ind}\)
• Relative topological properties and relative topological spaces
• General hypergeometric functions of matrices and their connection to representations of linear groups and Lie algebras
• Pseudocompactness and uniform continuity in topological groups
• Extensions of zero-sets and of real-valued functions
• On the dimension of homogeneous spaces
• Some theorems in dimension theory for normal Hausdorff spaces
• LOCAL DIMENSION OF NORMAL SPACES
• On the dimension of compact spaces
• Compactness type properties in topological groups
• Dimension of non-normal spaces
• Filter characterizations of z-, C*-, and C-embeddings
• Spaces in Which Special Sets are z-Embedded
• Nonequality of Dimensions for Metric Spaces
• Σ-spaces
• Varieties of topological groups III
• Ultrafilters and Compactification of Uniform Spaces
• Mapping Theorems for Non-Compact Spaces
• On the dimension of normal spaces
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