T0-spaces and pointwise convergence

Abstract The purpose of this paper is to give several different characterizations of those T 0 -spaces E with the property that if F : X × E → Y is separately continuous, then it is jointly continuous. One such is that the lattice 0( E ) of open sets of E be a hypercontinuous lattice (i.e. the interval topology on 0( E ) is Hausdorff). If E is a sober space, then E must be a quasicontinuous poset endowed with the Scott topology.