Abstract
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.
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Maslyuchenko, V.K., Nesterenko, V.V. Joint Continuity and Quasicontinuity of Horizontally Quasicontinuous Mappings. Ukrainian Mathematical Journal 52, 1952–1955 (2000). https://doi.org/10.1023/A:1010468229216
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DOI: https://doi.org/10.1023/A:1010468229216