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Proceedings of the American Mathematical Society

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



Product spaces in locales

Author: John Isbell
Journal: Proc. Amer. Math. Soc. 81 (1981), 116-118
MSC: Primary 54B10
MathSciNet review: 589150
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Abstract: The embedding of sober spaces in locales preserves products $ X \times Y$ where $ X$ is quasi-locally compact. A completely regular space $ X$ has this preservation property, for all $ Y$, if and only if $ X$ is a complemented sublocale of a compact space. Equivalently, every closed subset of $ X$ is locally compact somewhere.

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

  • [1] J. Benabou, Treillis locaux et paratopologies, Séminaire C. Ehresmann, 1957/58, Fac. des Sciences de Paris, 1959. MR 0121774 (22:12508)
  • [2] C. H. Dowker and D. Strauss, Sums in the category of frames, Houston J. Math. 3 (1977), 17-32. MR 0442900 (56:1275)
  • [3] K. H. Hofmann and J. D. Lawson, Irreducibility and generation in continuous lattices, Semigroup Forum 13 (1977), 307-353. MR 0434904 (55:7868)
  • [4] J. R. Isbell, Atomless parts of spaces, Math. Scand. 31 (1972), 5-32. MR 0358725 (50:11184)
  • [5] Z. Shmuely, The structure of Galois connections, Pacific J. Math. 54 (1974), 209-225. MR 0376455 (51:12630)

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Keywords: Locale, quasi-locally compact
Article copyright: © Copyright 1981 American Mathematical Society

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