Sequential closure of the space of jointly continuous functions in the space of separately continuous functions

• Date: 2016
• Main Authors: Voloshyn, H. A., Maslyuchenko, V. K., Волошин, Г. А., Маслюченко, В. К.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1830
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Given compact spaces $X$ and $Y$, we study the space $S(X \times Y )$ of separately continuous functions $f : X \times Y \rightarrow R$ endowed with the locally convex topology generated by the seminorms $|| f||^x = \mathrm{max}_{y \in Y} |f(x, y)|,\; x \in X$, and $|| f||_y = \mathrm{max}_{x \...