Abstract

In this paper,we introduced the star version of the Hurewicz basis covering property,studied by Babinkostova, Ko?cinac, and Scheepers in 2004. The authors obtained the relationship between star-selection principles and the star version of the Hurewicz basis covering property for metrizable spaces. We also consider the star version of Hurewicz measure zero spaces and characterized these new spaces by the star-selection principle related to star-Hurewicz spaces.

Highlights

  • The study of topological properties via various changes is not a new idea in topological spaces

  • The study of selection principles in topology and their relations to game theory and Ramsey theory was started by Scheepers [16]

  • The study of covering properties hsa become an active area for research

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Summary

Introduction

The study of topological properties via various changes is not a new idea in topological spaces. [20] A space X is said to have the Hurewicz property if for each sequence < Un : n ∈ ω > of open covers each x ∈ X

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