Quasicontinuous functions and the topology of pointwise convergence

Abstract

Let X be a Hausdorff topological space and let Q(X,R) be the space of all quasicontinuous functions on X with values in R and τp be the topology of pointwise convergence. We prove that Q(X,R) is dense in RX equipped with the product topology. We characterize some cardinal invariants of (Q(X,R),τp). We also compare cardinal invariants of (Q(R,R),τp) and (C(R,R),τp), the space of all continuous functions on R with values in R.