Joint Continuity and Quasicontinuity of Horizontally Quasicontinuous Mappings - Maslyuchenko, V. K.; Nesterenko, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2000)
We show that if Xis a topological space, Ysatisfies the second axiom of countability, and Zis a metrizable space, then, for every mapping f: X× Y→ Zthat is horizontally quasicontinuous and continuous in the second variable, a set of points x∈ Xsuch that fis continuous at every point from {x} × Yis residual in X. We also generalize a result of Martin concerning the quasicontinuity of separately quasicontinuous mappings.