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Certain subsets of products of $ \theta $-refinable spaces are realcompact


Author: Phillip Zenor
Journal: Proc. Amer. Math. Soc. 40 (1973), 612-614
MSC: Primary 54D60
MathSciNet review: 0322812
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Abstract: It is shown that the normal $ {T_1}$-space $ X$ is realcompact if and only if (a) each discrete subset of $ X$ is realcompact and (b) $ X$ can be embedded as a closed subset in the product of a collection of regular $ \theta $-refinable spaces.


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

  • [1] Dennis K. Burke, On 𝑝-spaces and 𝑤Δ-spaces, Pacific J. Math. 35 (1970), 285–296. MR 0278255
  • [2] 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
  • [3] R. L. Moore, Foundations of point set topology, Amer. Math. Soc. Colloq, Publ., vol. 13, Amer. Math. Soc., Providence, R.I., 1932.
  • [4] J. M. Worrell Jr. and H. H. Wicke, Characterizations of developable topological spaces, Canad. J. Math. 17 (1965), 820–830. MR 0182945
  • [5] Phillip Zenor, Certain subsets of products of metacompact spaces and subparacompact spaces are realcompact, Canad. J. Math. 24 (1972), 825–829. MR 0309070
  • [6] R. Haydon, Compactness in spaces of measures and measurecompact spaces (submitted for publication).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1973-0322812-9
Keywords: Realcompact, $ \theta $-refinable
Article copyright: © Copyright 1973 American Mathematical Society