On localization of the star-Menger selection principle

Abstract

In this paper we primarily introduce the local version of star-Menger property, namely locally star-Menger property (a space with this property is called locally star-Menger) and present some important topological observations. Certain interactions between the new notion and star-Menger property are also observed. Some observations on effectively locally star-Menger Pixley-Roy hyperspaces (introduced here) are obtained. Preservation like properties under several topological operations are also interpreted carefully. Besides, several results on decomposition and remainder of locally star-Menger spaces are also presented.

On certain star versions of the Scheepers property

“…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]).…”

Further investigations on certain star selection principles

“…The study of star selection principles is well known. For recent development of star selection principles one can consult the papers [1,6,9,12,13,16,18,19,22] and references therein. Let A and B be collections of families of subsets of an infinite space X.…”