Cardinal functions F_θ(X) and t_θ(X) for H-closed spaces

2012/06/28 by Filippo Cammaroto, Cammaroto, Filippo, Andrei Catalioto +3
Decision Sciences · Mathematics · #54A25 #54D10 #54D25 #54D35 #54G20 #Advanced Topology and Set Theory #FOS: Mathematics #Fuzzy and Soft Set Theory #General Topology (math.GN) #Rings, Modules, and Algebras #math.GN #msc:54A25 #msc:54D10 #msc:54D25 #msc:54D35 #msc:54G20

paper · pdf · doi:10.48550/arxiv.1206.6555

This paper has been withdrawn by the author due to an error in chapter 4

openalex publication_date 2012/06/28 · arxiv created 2012/12/17 · arxiv updated 2012/12/19 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

In this article, starting with results from a paper by Cammaroto and Kočinac in 1993, we prove that t_θ(X) = t_θ(X_s) = t(X_s) = F_θ(X) = F_θ(X_s) = F(X_s) for every H-closed and Urysohn space and we present some useful examples to study the full relationships among the cardinal functions t, t_θ, F and F_θ in the context of H-closed and Urysohn spaces. Also, we construct an H-closed space H for which F_θ(H) < t_θ(H). Two questions posed by Cammaroto and Kočinac about H-closed spaces are answered.

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