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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.

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]