On set-star-C-Menger spaces

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Motivated by the Arhangel’skii [2] “s-Lindelöf cardinal function” and Kočinac, Konca, and Singh [15] set-star covering properties, we introduce the setstar-C-Menger property. A space X is said to have the set-star-C-Menger property if for each nonempty subset A of X and each sequence of families of open subsets of X such that for each n ∈ ℕ, there is a sequence (Kn : n ∈ ℕ) of countably compact subsets of X such that . In this paper, we investigate the relationship between the set-star-C-Menger and other related properties and study the topological properties of the set-star-C-Menger property.