Search

Bài toán về sự bảo tồn các tính chất topo thông qua các ánh xạ là một trong những bài toán trọng tâm của topo đại cương. Vào năm 2015, Y. K. Song và R. Li đã chứng minh rằng, không gian Hurewicz yếu được bảo tồn qua ánh xạ liên tục ([1]). Gần đây, các tác giả khác cũng đã chỉ ra rằng, các không gian như star-C-Hurewicz, -Hurewiz yếu, star- -Hurewicz mạnh, star- -Hurewicz yếu, set star-Hurewicz, set star-Hurewicz mạnh được bảo tồn qua ánh xạ liên tục ([2], [3], [4]). Trong bài báo này, nhóm tác giả tiếp tục nghiên cứu sự bảo tồn qua ánh xạ liên tục của một số không gian topo được giới thiệu gần đây. Chứng rằng các không gian starcompact, star-Lindelöf, starcompact mạnh, star-Lindelöf mạnh, cellular-compact, cellular-Lindelöf, -starcompact, -starcompact, star-Menger và star-Menger mạnh cũng bảo tồn qua ánh xạ liên tục. Nhờ các kết quả này, nghiên cứu thu được rằng nếu một không gian là starcompact (tương ứng, star-Lindelöf, starcompact mạnh, star-Lindelöf mạnh, cellular-compact, cellular-Lindelöf, -starcompact, -starcompact, star-Menger, star-Menger mạnh), thì không gian thương nó cũng vậy.

A space X is said to be star-σ-countably compact if for every open cover U of X, there exists a σ-countably compact subset C of X such that St(C, U) = X. In this paper, we investigate the relationship between star-σ-countably compact spaces and other related spaces and also study the topological properties of star-_-countably compact spaces. [ABSTRACT FROM AUTHOR]

Motivated by the Arhangel'skii (Dokl Akad Nauk SSSR 175:751–754, 1967) "sLindelöf cardinal function" definition. We introduce some new covering properties called set starcompactness and set strongly starcompactness. We investigate their relationship to other related properties and study the topological properties of set starcompactness and set strongly starcompactness. Some open problems are posed. [ABSTRACT FROM AUTHOR]

We introduce two new notions of topological spaces called a countably starcompact space and a countably absolutely countably compact (= countably acc) space. We clarify the relations between these spaces and other related spaces and investigate topological properties of countably starcompact spaces and countably acc spaces. Some examples showing the limitations of our results are also given.

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.

A space X is star-K-Menger if for each sequence (Un : n ∈ N) of open covers of X there exists a sequence (Un : n ∈ N) of compact subsets of X such that {St(Kn, Un) : n ∈ N} is an open cover of X. In this paper, we construct an example of a Hausdorff star-Menger space that is not star-K- Menger which gives an answer to a question of Song [12], and continue to investigate topological properties of star-K-Menger spaces. [ABSTRACT FROM AUTHOR]

A space X is star-C-Menger if for each sequence (Un:n∈ ℕ) of open covers ofXthere exists a sequence (Kn:n∈ ℕ) of countably compact subsets ofXsuch that {St(Kn,Un) :n∈ ℕ} is an open cover ofX. In this paper, we investigate the relationship between star-C-Menger spaces and related spaces, and study topological properties of star-C-Menger spaces. [ABSTRACT FROM AUTHOR]

Abstract: A space X is absolutely strongly star-Menger if for each sequence of open covers of X and each dense subset D of X, there exists a sequence of finite subsets of D such that is an open cover of X. In this paper, we investigate the relationships between absolutely strongly star-Menger spaces and related spaces, and also study topological properties of absolutely strongly star-Menger spaces. [Copyright &y& Elsevier]

We prove some propositions and present some examples concerning the properties between countably compact and pseudocompact and the properties between Lindelöf and pseudo-Lindelöf. [ABSTRACT FROM AUTHOR]