$\beta$-Menger and $\beta$-Hurewicz spaces

Year 2022, Volume: 51 Issue: 1, 1 - 7, 14.02.2022

Memet Kule

https://doi.org/10.15672/hujms.911145

Abstract

Recently, some papers on weaker forms of classical covering properties of Hurewicz and Menger have been published. In this paper, using the covers formed by $\beta $-open sets, we introduce and study the properties of $\beta $-Menger and $\beta $-Hurewicz topological spaces. We give counterexamples that show the interrelations between those properties. The subject of our investigation is also the preservation of $\beta $-Menger and $\beta $-Hurewicz properties under subspaces, products, and mappings.

Keywords

β-open set, β-Menger space, β-Hurewicz space

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