On certain star versions of the Scheepers property

TL;DR

This paper introduces and explores star versions of the Scheepers property, analyzing their implications on critical cardinalities and examining related spaces and game-theoretic aspects.

Contribution

It introduces new star variants of the Scheepers property and investigates their properties, relationships, and implications in topology.

Findings

Analysis of critical cardinalities for star-Scheepers properties

Results on Isbell-Mrówka spaces, Niemytzki plane, and Alexandroff duplicates

Study of game-theoretic aspects of star-Scheepers properties

Abstract

The star versions of the Scheepers property, namely star-Scheepers, strongly star-Scheepers and new star-Scheepers property have been introduced. We explore further ramifications concerning critical cardinalities. Quite a few interesting observations are obtained while dealing with the Isbell-Mr\'{o}wka spaces, Niemytzki plane and Alexandroff duplicates. The properties like monotonically normal, locally countable cellularity (which is introduced here) play an important role in our investigation. We study games corresponding to the classical and star variants of the Scheepers property which have not been investigated in prior works. Some open problems are also posed.