A study of remainders of topological groups

A. V. Arhangel'skii

Displaying similar documents to “A study of remainders of topological groups”

On hereditarily normal topological groups

(2012)

Fundamenta Mathematicae

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We investigate hereditarily normal topological groups and their subspaces. We prove that every compact subspace of a hereditarily normal topological group is metrizable. To prove this statement we first show that a hereditarily normal topological group with a non-trivial convergent sequence has $G_{δ}$ -diagonal. This implies, in particular, that every countably compact subspace of a hereditarily normal topological group with a non-trivial convergent sequence is metrizable. Another corollary...

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

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

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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...

Extensions of topological and semitopological groups and the product operation

Aleksander V. Arhangel&#039;skii, Miroslav Hušek (2001)

Commentationes Mathematicae Universitatis Carolinae

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The main results concern commutativity of Hewitt-Nachbin realcompactification or Dieudonné completion with products of topological groups. It is shown that for every topological group $G$ that is not Dieudonné complete one can find a Dieudonné complete group $H$ such that the Dieudonné completion of $G \times H$ is not a topological group containing $G \times H$ as a subgroup. Using Korovin’s construction of $G_{δ}$ -dense orbits, we present some examples showing that some results on topological groups are not valid...

Topological Rough Groups

Nurettin Bağırmaz, İlhan İçen, Abdullah F. Özcan (2016)

Topological Algebra and its Applications

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The concept of topological group is a simple combination of the concepts of abstract group and topological space. The purpose of this paper is to combine the concepts of topological space and rough groups; called topological rough groups on an approximation space.

Alexandroff One Point Compactification

Czesław Byliński (2007)

Formalized Mathematics

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In the article, I introduce the notions of the compactification of topological spaces and the Alexandroff one point compactification. Some properties of the locally compact spaces and one point compactification are proved.