On θ-Hurewicz and α-Hurewicz Topological spaces

2023/07/02 by Gaurav Kumar, Kumar, Gaurav, Sumit Mittal +3
Decision Sciences · Mathematics · #54C08 #54D10 #54D20 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Secondary 54A10

paper · pdf · doi:10.48550/arxiv.2307.00487

openalex publication_date 2023/07/02 · openalex created_date 2023/07/05 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduced α-Hurewicz & θ-Hurewicz properties in a topological space X and investigated their relationship with other selective covering properties. We have shown that for an extremally disconnected semi-regular spaces, the properties: Hurewicz, semi-Hurewicz, α-Hurewicz, θ-Hurewicz, almost-Hurewicz, nearly Hurewicz and midly Hurewicz are equivalent. We have also proved that for an extremally disconnected space X, every finite power of X has θ-Hurewicz property if and only if X has the selection principle U_fin(θ-Ω, θ-Ω). The preservation under several types of mappings of α-Hurewicz and θ-Hurewicz properties are also discussed. Also, we showed that, if X is a mildly Hurewicz subspace of ω^ω, than X is bounded.

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