Namioka spaces and topological games

TL;DR

This paper introduces a new class of topological spaces called $eta-v$-unfavorable spaces, proving they are Namioka spaces and thus have desirable joint continuity properties for functions on product spaces.

Contribution

It defines the class of $eta-v$-unfavorable spaces and proves they are Namioka spaces, extending known classes of spaces with joint continuity properties.

Findings

$eta-v$-unfavorable spaces are Namioka spaces

Every $eta-v$-unfavorable space ensures joint continuity on a dense $G_\delta$-set

The class contains some known $eta$-unfavorable spaces

Abstract

We introduce a class of $\beta-v$-unfavorable spaces, which contains some known classes of $\beta$-unfavorable spaces for topological games of Choquet type. It is proved that every $\beta-v$-unfavorable space $X$ is a Namioka space, that is for any compact space $Y$ and any separately continuous function $f:X\times Y\to \mathbb R$ there exists a dense in $X$ $G_{\delta}$-set $A\subseteq X$ such that $f$ is jointly continuous at each point of $A\times Y$.