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Norm continuity of quasicontinuous mappings into $C_p(Y)$

Volume 154 / 2018

Ľubica Holá, Alireza Kamel Mirmostafaee Colloquium Mathematicum 154 (2018), 97-105 MSC: Primary 54C08, 54C05; Secondary 54E52. DOI: 10.4064/cm7162-12-2017 Published online: 2 August 2018


We use a topological game argument to show that, under some restrictions on a topological space $X$, every quasicontinuous mapping $\varphi :X \to C_p(Y)$ is norm continuous at points of a dense $G_\delta $ subset of $X$ provided that $Y$ is totally countably compact. We improve some old results on joint continuity of separately continuous functions by J. Saint-Raymond [Proc. Amer. Math. Soc. 87 (1983), 499–504].


  • Ľubica HoláMathematical Institute
    Slovak Academy of Sciences
    Štefánikova 49
    814 73 Bratislava, Slovakia
  • Alireza Kamel MirmostafaeeCenter of Excellence in Analysis on Algebraic Structures
    Department of Pure Mathematics
    Ferdowsi University of Mashhad
    P.O. Box 1159
    Mashhad 91775, Iran

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