On countable tightness type properties of spaces of quasicontinuous functions

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. $S_1(K, K)$, $K_{\Omega}$-Lindelofness, $S_1(K_{\Omega}, K_{\Omega})$) were defined by M. Scheepers and studied in theory of selection principles in the class of metric spaces. For any cardinal number $\kappa$, we get a functional characterization of $\kappa^+$-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.