Some remarks on games of certain star selection principles

On certain star versions of the Scheepers property

“…If we consider |A| = ω 1 , then AD(Ψ(A)) does not satisfy * U fin (O, Ω) as A×{1} = {(A, 1) : A ∈ A} is a discrete clopen subset of AD(X) with cardinality ω 1 . The following result is similar to Theorem 3.34(1).…”

“…Proof. We only present proof for (1). Let κ be a cardinal smaller than d and X = ∪ α<κ X α , where each X α is star-Hurewicz.…”

“…Next we use the idea of [1,14] It can be seen that the games RG ufin (O, Ω), RG * ufin (O, Ω) and RSG * fin (O, Ω) are all equivalent for paracompact Hausdorff spaces. Similar such investigations may be carried out in line of [1].…”

“…In [1], we recently investigated on games of some star selection principles. A similar type of investigation for the star versions of the Scheepers property has been carried out in this section.…”

“…star selection principles and new star selection principles may consult the papers [1,5,6,11,12,18,19,24,31] where more references can be found. Note that one of the most important selection principle is U fin (O, Ω), nowadays called the Scheepers property (see [17,25]).…”