Linearly ordered compacts and co-Namioka spaces

TL;DR

This paper proves that any linearly ordered compact space is a co-Namioka space, showing that for Baire spaces and separately continuous functions, joint continuity occurs densely.

Contribution

It establishes that all linearly ordered compact spaces are co-Namioka spaces, extending the class of spaces with dense joint continuity for separately continuous functions.

Findings

Existence of a dense G_delta set where functions are jointly continuous

Any linearly ordered compact is a co-Namioka space

Joint continuity occurs densely in the product space

Abstract

It is shown that for any Baire space $X$, linearly ordered compact $Y$ and separately continuous mapping $f:X\times Y\to\mathbb R$ there exists a dense in $X$ $G_\delta$-set $A\subseteq X$ such that $f$ is jointly continuous at every point of $A\times Y$, i.e. any linearly ordered compact is a co-Namioka space.