Linearly ordered compact sets and co-Namioka spaces - Mykhailyuk, V. V. (Ukrains’kyi Matematychnyi Zhurnal, 2007)
It is proved that for any Baire space $X$, linearly ordered compact $Y$, and separately continuous mapping $f:\, X \times Y \rightarrow \mathbb{R}$, there exists a $G_{\delta}$-set $A \subseteq X$dense in $X$ and such that $f$ is jointly continuous at every point of the set $A \times Y$, i.e., any linearly ordered compact is a co-Namioka space.