On countable tightness type properties of spaces of quasicontinuous functions

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. $S_1(K,K)$, $K_{\mathrm{\Omega }}$-Lindelofness, $S_1(K_{\mathrm{\Omega }},K_{\mathrm{\Omega }})$) 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.