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arXiv · 2311.07517

On countable tightness type properties of spaces of quasicontinuous functions

Alexander V. Osipov
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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 $T_2$-space $X$ into the discrete two-point space $\{0, 1\}$ through properties of $X$ determined by selection principles. These properties (e.g. $S_1(K, K)$, $K_Ω$-Lindelofness, $S_1(K_Ω, K_Ω)$) 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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Alexander V. Osipov. 2024-01-26. On countable tightness type properties of spaces of quasicontinuous functions. https://arxiv.org/abs/2311.07517

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