Tightness type properties of spaces of quasicontinuous functions

Abstract

Using approximation by continuous functions we prove the following statements to types of tightness in a space $Q_p(X, \mathbb{R})$ of all quasicontinuous real-valued functions with the topology $\tau_p$ of pointwise convergence: the countability of tightness (fan-tightness, strong fan-tightness) at a point $f$ of space $Q_p(X, \mathbb{R})$ implies the countability of tightness (fan-tightness, strong fan-tightness) of space $Q_p(X,Y)$ of all quasicontinuous functions from $X$ into any non-one-point metrizable space $Y$. This result is the answer to the open question in the class of metrizable spaces.