Fréchet-Urysohn property of quasicontinuous functions

The aim of this paper is to study the Fréchet-Urysohn property of the space Q p (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 Q p (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 Q p (X,R) is Fréchet-Urysohn if and only if X is countable. 2010 MSC: 54C35, 54C40