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Proceedings of the American Mathematical Society

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Pseudocompact spaces and functionally determined uniformities

Author: Rodolfo Talamo
Journal: Proc. Amer. Math. Soc. 56 (1976), 318-320
MSC: Primary 54E15; Secondary 54C30
MathSciNet review: 0407808
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Abstract: A topological space is pseudocompact if and only if every admissible uniformity is functionally determined. We construct, on the discrete countable space $N$, an admissible (pseudo)-metric uniformity which is not functionally determined.

References [Enhancements On Off] (What's this?)

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  • Masahiko Atsuji, Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 11–16; erratum, 941. MR 99023
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Keywords: Pseudocompact space, functionally determined uniformity, <IMG WIDTH="22" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img1.gif" ALT="$C$">-embedding, <IMG WIDTH="17" HEIGHT="20" ALIGN="BOTTOM" BORDER="0" SRC="images/img2.gif" ALT="$u$">-embedding
Article copyright: © Copyright 1976 American Mathematical Society