On set-star-K-Menger spaces

A topological space X is said to have the set-star-K-Menger property if for each nonempty subset A of X and for each sequence (U-n : n is an element of N) of open families in X such that (A) over bar subset of boolean OR U-n for all n is an element of N, there is a sequence (K-n : n is an element of N) of compact subsets of X such that (Lambda) over bar subset of boolean OR(n is an element of N) St(K-n, U-n). This property is motivated by the sLindelof cardinal function in Arhangel'skii [1] and set-star covering properties introduced by Kocinac, Konca and Singh [10]. We investigate the relationships between the set-star-K-Menger and other related properties, and study the topological properties of the set-star-K-Menger property.