Nearly H-closed spaces

Osipov, Alexander V.

doi:10.1007/s10958-008-9234-9

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…H-closed topological spaces in terms of θ-accumulation points were investigated in [7,16,17,19,21,22,28,29]. Also observe that each H-closed space is feebly compact.…”

Section: Preliminariesmentioning

confidence: 99%

“…Observe that if a topological space X is regular then each closed subset A of X is θ-closed. A topological space X is called weakly H-closed if each ω-filter F has a θ-accumulation point in X. Generalizations of H-closed spaces were investigated by Osipov in [19,20]. Obviously, for a topological space X the following implications hold: X is Hclosed ⇒ X is weakly H-closed ⇒ X is feebly compact.…”

Section: Proposition 25 Lemma 32 and Remark 33 Imply The Followingmentioning

confidence: 99%

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Closed subsets of compact-like topological spaces

Bardyla

Ravsky²

2020

Appl. Gen. Topol.

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<p>We investigate closed subsets (subsemigroups, resp.) of compact-like topological spaces (semigroups, resp.). We show that each Hausdorff topological space is a closed subspace of some Hausdorff ω-bounded pracompact topological space and describe open dense subspaces of<br />countably pracompact topological spaces. We construct a pseudocompact topological semigroup which contains the bicyclic monoid as a closed subsemigroup. This example provides an affirmative answer to a question posed by Banakh, Dimitrova, and Gutik in [4]. Also, we show that the semigroup of ω×ω-matrix units cannot be embedded into a Hausdorff topological semigroup whose space is weakly H-closed.</p>

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“…H-closed topological spaces in terms of θ-accumulation points were investigated in [7,16,17,19,21,22,28,29]. Also observe that each H-closed space is feebly compact.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Proposition 25 Lemma 32 and Remark 33 Imply The Followingmentioning

confidence: 99%

Closed subsets of compact-like topological spaces

Bardyla

Ravsky²

2020

Appl. Gen. Topol.

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“…• for each open cover F = {F α } α∈A of X there exists a finite subset B ⊂ A such that ∪ α∈B F α = X. H-closed topological spaces in terms of θ-accumulation points were investigated in [8,17,18,20,22,23,29,30]. Also recall that each H-closed space is feebly compact.…”

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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“…In 1966 Velichko [29] introduced the notion of θ-closedness. For a subset M of a topological space X the θ-closure is defined by cl θ M = {x ∈ X : every closed neighborhood of x meets M}, M is θ-closed if cl θ M = M. This concept was used by many authors for the study of Hausdorff nonregular spaces [9,11,13,14,27,28] and [16][17][18][19][20][21][22][23]. The S(n)-spaces were introduced by Viglino in 1969 (see [30]) under the name T n -spaces.…”

Section: Introductionmentioning

confidence: 99%

On the cardinality of S(n)-Spaces

Osipov

2019

Quaestiones Mathematicae

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In this paper, for a topological space X and any positive integer n, we define the cardinal functions sL θ(n) (X), θ(n)-quasi-Menger number qM θ(n) (X) and s(n)-quasi-Menger number qM s(n) (X). We prove the following statements:• For every S(2n)-space X, |X| ≤ 2 sL θ(n) (X)κ θ(n) (X) .• For every S(2n)-space X, |X| ≤ 2 qM θ(n) (X)κ θ(n) (X) .• For every S(2n)-space X, |X| ≤ 2 qM s(n) (X)κ θ(n) (X) . Similar results are stated for S(2n − 1)-spaces.

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Nearly H-closed spaces

Cited by 4 publications

References 7 publications

Closed subsets of compact-like topological spaces

Closed subsets of compact-like topological spaces

Closed subsets of compact-like topological spaces

On the cardinality of S(n)-Spaces

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