A space X is absolutely strongly star-Hurewicz if for each sequence (Un :n ∈ℕ/ of open covers of X and each dense subset D of X, there exists a sequence (Fn :n ∈ℕ/ of finite subsets of D such that for each x ∈X, x ∈St(Fn; Un) for all but finitely many n. In this paper, we investigate the relationships between absolutely strongly star-Hurewicz spaces and related spaces, and also study topological properties of absolutely strongly star-Hurewicz spaces.
We prove the following statements: (1) every Tychonoff linked-Lindelöf (centered-Lindelöf, star countable) space can be represented as a closed subspace in a Tychonoff pseudocompact absolutely star countable space; (2) every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented as a closed G δ-subspace in a Hausdorff (regular, Tychonoff) absolutely star countable space; (3) there exists a pseudocompact absolutely star countable Tychonoff space having a regular closed subspace which...
A space X is star-Hurewicz if for each sequence (𝒰ₙ: n ∈ ℕ) of open covers of X there exists a sequence (𝓥ₙ: n ∈ ℕ) such that for each n, 𝓥ₙ is a finite subset of 𝒰ₙ, and for each x ∈ X, x ∈ St(⋃ 𝓥ₙ,𝒰ₙ) for all but finitely many n. We investigate the relationship between star-Hurewicz spaces and related spaces, and also study topological properties of star-Hurewicz spaces.
A space is -starcompact if for every open cover of there exists a Lindelöf subset of such that We clarify the relations between -starcompact spaces and other related spaces and investigate topological properties of -starcompact spaces. A question of Hiremath is answered.
In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed subspace.
A space is if for every open cover of and every dense subset of , there exists a countable subset of such that is discrete closed in and , where . We show that every Hausdorff star-Lindelöf space can be represented in a Hausdorff discretely absolutely star-Lindelöf space as a closed subspace.
A space is strongly star-Menger if for each sequence of open covers of , there exists a sequence of finite subsets of such that is an open cover of . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.
In this paper, we prove the following statements: (1) For any cardinal , there exists a Tychonoff star-Lindelöf space such that . (2) There is a Tychonoff discretely star-Lindelöf space such that does not exist. (3) For any cardinal , there exists a Tychonoff pseudocompact -starcompact space such that .
In this paper, we prove the following statements: (1) There exists a Tychonoff star countable discrete closed, pseudocompact space having a regular-closed subspace which is not star countable. (2) Every separable space can be embedded into an absolutely star countable discrete closed space as a closed subspace. (3) Assuming , there exists a normal absolutely star countable discrete closed space having a regular-closed subspace which is not star countable.
Let be a topological property. A space is said to be star P if whenever is an open cover of , there exists a subspace with property such that . In this note, we construct a Tychonoff pseudocompact SCE-space which is not star Lindelöf, which gives a negative answer to a question of Rojas-Sánchez and Tamariz-Mascarúa.
In this paper, we generalize Vaughan's and Bonanzinga's results on absolute countable compactness of product spaces and give an example of a separable, countably compact, topological group which is not absolutely countably compact. The example answers questions of Matveev [8, Question 1] and Vaughan [9, Question (1)].
In this paper, we prove the following statements: (1) For every regular uncountable cardinal , there exist a Tychonoff space and a subspace of such that is both relatively absolute star-Lindelöf and relative property (a) in and , but is not strongly relative star-Lindelöf in and is not star-Lindelöf. (2) There exist a Tychonoff space and a subspace of such that is strongly relative star-Lindelöf in (hence, relative star-Lindelöf), but is not absolutely relative star-Lindelöf...
Let be a topological property. A space is said to be star if whenever is an open cover of , there exists a subspace with property such that , where In this paper, we study the relationships of star properties for in pseudocompact spaces by giving some examples.
A space is if for every open cover of there exists a countably compact subset of such that In this paper we investigate the relations between -starcompact spaces and other related spaces, and also study topological properties of -starcompact spaces.
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