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Proceedings of the American Mathematical Society

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A non-Hausdorff Ascoli theorem for $ k\sb{3}$-spaces


Authors: Geoffrey Fox and Pedro Morales
Journal: Proc. Amer. Math. Soc. 39 (1973), 633-636
MSC: Primary 54C35
DOI: https://doi.org/10.1090/S0002-9939-1973-0391004-X
MathSciNet review: 0391004
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Abstract: The paper establishes an Ascoli theorem in the space of continuous functions on a $ {k_3}$-space to a regular space. The theorem, in terms of even continuity and the compact open topology $ {\tau _c}$, properly contains the Ascoli theorems of Myers, Gale, Kelley-Morse, Bagley-Yang, and the $ {k_3}$-space theorem of Noble.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0391004-X
Keywords: $ k$-space, $ {k_3}$-space, even continuity, compact open topology, $ R$-saturation
Article copyright: © Copyright 1973 American Mathematical Society