Linearly ordered compact sets and co-Namioka spaces

We prove that, for an arbitrary Baire space X, a linearly ordered compact set Y, and a separately continuous mapping ƒ: X × Y → R, there exists a G _δ-set A ⊆ X dense in X and such that the function ƒ is jointly continuous at every point of the set A × Y, i.e., any linearly ordered compact set is a co-Namioka space. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 1001–1004, July, 2007.