On old and new classes of feebly compact spaces

Гутік, Олег; Ravsky, Oleksandr

doi:10.30970/vmm.2018.85.048-059

Cited by 11 publications

(9 citation statements)

References 17 publications

(23 reference statements)

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“…Therefore, topologists often investigate various classes of compact-like spaces and relations between them, see, for instance, basic [Eng,Chap. 3] and general works [vDRRT], [Mat], [Vau], [Ste], [Lip], [GR2]. In the present paper we will consider some of compact-like properties.…”

Section: Definitionsmentioning

confidence: 99%

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Positive answers to Koch’s problem in special cases

Банах

Bardyla

Guran

et al. 2020

Topological Algebra and Its Applications

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A topological semigroup is monothetic provided it contains a dense cyclic subsemigroup. The Koch problem asks whether every locally compact monothetic monoid is compact. This problem was opened for more than sixty years, till in 2018 Zelenyuk obtained a negative answer. In this paper we obtain a positive answer for Koch's problem for some special classes of topological monoids. Namely, we show that a locally compact monothetic topological monoid is a compact topological group if and only if S is a submonoid of a quasitopological group if and only if S has open shifts if and only if S is non-viscous in the sense of Averbukh. The last condition means that any neighborhood U of the identity 1 of S and for any element a ∈ S there exists a neighborhood V of a such that any element x ∈ S with (xV ∪ V x) ∩ V = ∅ belongs to the neighborhood U of 1.

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Section: Definitionsmentioning

confidence: 99%

“…Some of them are presented at Diagram 3 in [Mat,p.17], at Diagram 1 in [D-AS, p. 58] (for Tychonoff spaces), at Diagram 3.6 in [Ste,p. 611], and at Diagram in [GR2].…”

Section: Definitionsmentioning

confidence: 99%

Positive answers to Koch’s problem in special cases

Банах

Bardyla

Guran

et al. 2020

Topological Algebra and Its Applications

Self Cite

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show abstract

“…• d-compact, if for each continuous map f : X → d ω the image f (X) is finite. By [23], for a topological space X the following implications hold: X is compact ⇒ X is countably compact ⇒ X is countably pracompact ⇒ X is feebly compact ⇒ X is d-compact. Also, a feebly compact topological space X is pseudocompact iff X is Tychonoff.…”

Section: Preliminariesmentioning

confidence: 99%

Embedding of graph inverse semigroups into CLP-compact topological semigroups

Bardyla

2020

Topology and its Applications

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“…• feebly compact, if each open ω-filter on X has an accumulation point. The interplay between some of the above properties is shown in the diagram at page 3 in [14].…”

Section: Preliminariesmentioning

confidence: 99%

Closed subsets of compact-like topological spaces

Bardyla¹,

Ravsky²

2019

Preprint

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We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We prove that each Hausdorff topological space can be embedded as a closed subspace into an H-closed topological space. However, the semigroup of ω×ω-matrix units cannot be embedded into a topological semigroup which is a weakly H-closed topological space. We show that each Hausdorff topological space is a closed subspace of some ω-bounded pracompact topological space and describe open dense subspaces of countably pracompact topological spaces. Also, we construct a pseudocompact topological semigroup which contains the bicyclic monoid as a closed subsemigroup, providing a positive solution of a problem posed by Banakh, Dimitrova, and Gutik.

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On old and new classes of feebly compact spaces

Abstract: We introduce three new classes of countably pracompact spaces, consider their basic properties and relations with other compact-like spaces.

Cited by 11 publications

References 17 publications

Positive answers to Koch’s problem in special cases

Positive answers to Koch’s problem in special cases

Embedding of graph inverse semigroups into CLP-compact topological semigroups

Closed subsets of compact-like topological spaces

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