We study subgroups of Z which possess group theoretic properties analogous to properties introduced by Menger (1924), Hurewicz (1925), Rothberger (1938), and Scheepers (1996). The studied properties were introduced independently by Kočinac and Okunev. We obtain purely combinatorial characterizations of these properties, and combine them with other techniques to solve several questions of Babink...

*Correspondence: [email protected] 1Department of Mathematics, Nanchang University, Nanchang, 330031, P.R. China Full list of author information is available at the end of the article Abstract In this paper, a new concept of the common property (E.A) for two hybrid pairs of mappings is introduced in Menger PM-spaces. Utilizing this concept, some common fixed point theorems, which shed some new...

We study when the product of separable metric spaces has the selective screenability property, the Menger property, or the Rothberger property. Our results imply The product of a Lusin set and (1) a Sierpinski set always has the Menger property (Corollary 12); (2) a γ-set always has the Rothberger property (Corollary 13). All topological spaces considered in this paper are assumed to be separab...

Let PR(X) denote the hyperspace of non-empty finite subsets a topological space X with Pixley-Roy topology. In this paper, we investigate quasi-Rothberger property in PR(X). We prove that for X, followings are equivalent: (1) is quasi-Rothberger; (2) satisfies S1(?rc f?h,?wrc f?h); (3) separable and each co-finite subset S1(?pc f?h,?wpc (4) PR(Y) Y X. also characterize quasi-Menger quasi-Hurewi...

This article is a continuation of study star-Menger selection properties in line (Kocinac, 2009, 2015), where we mainly use covers consisting G? sets with certain additional condition. It observed that star-Mengerness equivalent to the fact every such type cover space has countable subcover. We improve this result by considering ?subcovers cardinality less than b? instead ?countable subcovers?,...

Around 1930, Menger expressed his interest in the concept of abstract angle function. He introduced a general definition this notion for metric and semi-metric spaces. also proposed two problems concerning conformal embeddability spaces endowed with an function into Euclidean These received attention later years but only some particular cases In article, we first update to apply larger class be...