Fréchet-Urysohn property of quasicontinuous functions

Abstract

The aim of this paper is to study the Fréchet-Urysohn property of the space Qp(X,R) of real-valued quasicontinuous functions, defined on a Hausdorff space X, endowed with the pointwise convergence topology. It is proved that under Suslin's Hypothesis, for an open Whyburn space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable. In particular, it is true in the class of first-countable regular spaces X. In ZFC, it is proved that for a metrizable space X, the space Qp(X,R) is Fréchet-Urysohn if and only if X is countable. 2010 MSC: 54C35, 54C40