Displaying similar documents to “Absolutely strongly star-Hurewicz spaces”

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

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A space X is strongly star-Menger if for each sequence ( 𝒰 n : n ) of open covers of X , there exists a sequence ( K n : n N ) of finite subsets of X such that { S t ( K n , 𝒰 n ) : n } is an open cover of X . 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.

Remarks on Star-Hurewicz Spaces

Yan-Kui Song (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

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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.