On countable tightness type properties of spaces of quasicontinuous functions

2023/11/13 by Alexander V. Osipov, Osipov, Alexander V.
Mathematics · #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #General Topology (math.GN) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2311.07517

openalex publication_date 2023/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we get characterizations countable tightness, countable fan-tightness and countable strong fan-tightness of spaces of quasicontinuous functions with the topology of pointwise convergence from a open Whyburn T₂-space X into the discrete two-point space \0, 1\ through properties of X determined by selection principles. These properties (e.g. S₁(K, K), K_Ω-Lindelofness, S₁(K_Ω, K_Ω)) were defined by M. Scheepers and studied in theory of selection principles in the class of metric spaces. For any cardinal number κ, we get a functional characterization of κ⁺-Lusin space in class of separable metrizable spaces through tightness of compact subsets of a space of quasicontinuous real-valued functions with the topology of pointwise convergence.

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