Abstract
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.
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References
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 7, pp. 1001–1004, July, 2007.
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Mykhailyuk, V.V. Linearly ordered compact sets and co-Namioka spaces. Ukr Math J 59, 1110–1113 (2007). https://doi.org/10.1007/s11253-007-0071-7
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DOI: https://doi.org/10.1007/s11253-007-0071-7