Characterization of quasi-continuity of multifunctions of two variables

Abstract

Abstract We prove that a compact-valued multifunction F: X × Y → Z, where X is a Baire space and Y, Z are separable metrizable spaces, is quasi-continuous if and only if F is horizontally quasi-continuous and there exists an residual subset M of X such that for any x ∈ M the multifunction F x = F(x, ·) is quasi-continuous on Y.