Displaying similar documents to “$g^\ast $-closed sets and a new separation axiom in Alexandroff spaces”

On pseudocompactness and related notions in ZF

Kyriakos Keremedis (2018)

Commentationes Mathematicae Universitatis Carolinae

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We study in ZF and in the class of T 1 spaces the web of implications/ non-implications between the notions of pseudocompactness, light compactness, countable compactness and some of their ZFC equivalents.

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...

Condensations of Tychonoff universal topological algebras

Constancio Hernández (2001)

Commentationes Mathematicae Universitatis Carolinae

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Let ( L , 𝒯 ) be a Tychonoff (regular) paratopological group or algebra over a field or ring K or a topological semigroup. If nw ( L , 𝒯 ) ≤ τ and nw ( K ) ≤ τ , then there exists a Tychonoff (regular) topology 𝒯 * ⊆ 𝒯 such that w ( L , 𝒯 * ) ≤ τ and ( L , 𝒯 * ) is a paratopological group, algebra over K or a topological semigroup respectively.