  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.

General Topology