Mildly version of Hurewicz Basis covering property and Hurewicz measure zero spaces

2022/02/25 by Manoj Bhardwaj, Bhardwaj, Manoj, Alexander V. Osipov +1
Mathematics · Decision Sciences · #Advanced Topology and Set Theory #Rings, Modules, and Algebras #Fuzzy and Soft Set Theory

paper · pdf · doi:10.48550/arxiv.2202.12652

Abstract

In this paper, we introduced the mildly version of the Hurewicz basis covering property, studied by Babinkostova, Kočinac, and Scheepers. A space X is said to have mildly-Hurewicz property if for each sequence ⟨ U_n : n∈ ω⟩ of clopen covers of X there is a sequence ⟨ V_n : n∈ ω⟩ such that for each n, V_n is a finite subset of U_n and for each x∈ X, x belongs to \bigcupV_n for all but finitely many n. Then we characterized mildly-Hurewicz property by mildly-Hurewicz Basis property and mildly-Hurewicz measure zero property for metrizable spaces.

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