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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.

In this paper, we show that assumingω1<, there exists a Tychonoff star-C-Menger space having a regular-closedGδ-subspace which is not star-C-Menger which gives a partial answer to a question of Song and Yin [12], and continue to investigate topological properties of star-C-Menger spaces. [ABSTRACT FROM PUBLISHER]

A spaceXisalmost Rothberger (weakly Rothberger)if for each sequence (un:n∊ ℕ) of open covers ofXthere exists a sequence (Un:n∊ ℕ) such that for every n ∊ ℕ,U∊unand ∪n∊ℕ=X(resp.,=X). In this paper, we investigate the relationships among Rothberger spaces, almost Rothberger spaces and weakly Rothberger spaces, and also study topological properties of almost Rothberger spaces and weakly Rothberger spaces. [ABSTRACT FROM PUBLISHER]

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]