Displaying similar documents to “Two types of remainders of topological groups”

On a theorem of W.W. Comfort and K.A. Ross

Aleksander V. Arhangel'skii (1999)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

A well known theorem of W.W. Comfort and K.A. Ross, stating that every pseudocompact group is C -embedded in its Weil completion [5] (which is a compact group), is extended to some new classes of topological groups, and the proofs are very transparent, short and elementary (the key role in the proofs belongs to Lemmas 1.1 and 4.1). In particular, we introduce a new notion of canonical uniform tightness of a topological group G and prove that every G δ -dense subspace Y of a topological group...

Moscow spaces, Pestov-Tkačenko Problem, and C -embeddings

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that there exists an Abelian topological group G such that the operations in G cannot be extended to the Dieudonné completion μ G of the space G in such a way that G becomes a topological subgroup of the topological group μ G . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions...

A study of remainders of topological groups

A. V. Arhangel'skii (2009)

Fundamenta Mathematicae

Similarity:

Some duality theorems relating properties of topological groups to properties of their remainders are established. It is shown that no Dowker space can be a remainder of a topological group. Perfect normality of a remainder of a topological group is consistently equivalent to hereditary Lindelöfness of this remainder. No L-space can be a remainder of a non-locally compact topological group. Normality is equivalent to collectionwise normality for remainders of topological groups. If a...

The Baire property in remainders of topological groups and other results

Aleksander V. Arhangel'skii (2009)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is established that a remainder of a non-locally compact topological group G has the Baire property if and only if the space G is not Čech-complete. We also show that if G is a non-locally compact topological group of countable tightness, then either G is submetrizable, or G is the Čech-Stone remainder of an arbitrary remainder Y of G . It follows that if G and H are non-submetrizable topological groups of countable tightness such that some remainders of G and H are homeomorphic, then...