In this paper our focus is to study certain covering properties in topological spaces by using semi-open covers. A part of this article deals with Rothberger-type covering properties. The notions of s-Rothberger, almost s-Rothberger, star s-Rothberger, almost star s-Rothberger, strongly star s-Rothberger spaces are defined and corresponding properties are investigated.

The aim of this note is to provide an answer a question posted in recent paper. In2018, after introducing the notion Ideal Rothberger space, author examines some properties ofthese spaces. Also there has been comparison spaces (X, τ ), and τ∗) terms being(ideal)Rothberger. According this, it shown that if then )is also Rothberger. Therefore, naturally asked that, one can find extra conditionsfo...

We give easy proofs that a) the Continuum Hypothesis implies that if the product of X with every Lindelöf space is Lindelöf, then X is a D-space, and b) Borel’s Conjecture implies every Rothberger space is Hurewicz.

Let PR(X) denote the hyperspace of nonempty finite subsets a topological spaceX with Pixley-Roy topology. In this paper, by introducing closed-miss-finite networks and using principle ultrafilters, we proved that following statements are equivalent for space X: (1) is weakly Rothberger; (2) X satisfies S1(?rcf ,?wrcf ); (3) separable ? {x} S1(?cf ,?wcf ) each x X; (4) principal ultrafilter F [x...

In this paper, selection principles are defined and studied in the realm of irresolute topological groups. Especially, s-Menger-bounded s-Rothberger-bounded type covering properties introduced studied.

A space X has the Rothberger property in all finite powers if, and only if, its collection of ω-covers has Ramseyan properties.

A space X has the Rothberger property in all finite powers if, and only if, its collection of ω-covers has Ramseyan properties.

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...

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

We obtain from the consistency of the existence of a measurable cardinal the consistency of “small” upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are Gδ sets. Call a topological space in which each singleton is a Gδ set a points Gδ space. A.V. Arhangel’skii proved that any points Gδ Lindelöf space must have cardinality less than the least measurable cardin...