Norm continuity of quasicontinuous mappings into $C_p(Y)$
Volume 154 / 2018
Colloquium Mathematicum 154 (2018), 97-105
MSC: Primary 54C08, 54C05; Secondary 54E52.
DOI: 10.4064/cm7162-12-2017
Published online: 2 August 2018
Abstract
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].
