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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Pseudocompact spaces and functionally determined uniformities


Author: Rodolfo Talamo
Journal: Proc. Amer. Math. Soc. 56 (1976), 318-320
MSC: Primary 54E15; Secondary 54C30
DOI: https://doi.org/10.1090/S0002-9939-1976-0407808-3
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?)

  • Richard A. Alò and Harvey L. Shapiro, Normal topological spaces, Cambridge University Press, New York-London, 1974. Cambridge Tracts in Mathematics, No. 65. MR 0390985
  • Masahiko Atsuji, Uniform continuity of continuous functions of metric spaces, Pacific J. Math. 8 (1958), 11–16; erratum, 941. MR 99023
  • James Dugundji, Topology, Allyn and Bacon, Inc., Boston, Mass.-London-Sydney, 1978. Reprinting of the 1966 original; Allyn and Bacon Series in Advanced Mathematics. MR 0478089
  • Leonard Gillman and Meyer Jerison, Rings of continuous functions, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto-London-New York, 1960. MR 0116199

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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