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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Embeddings in minimal Hausdorff spaces
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by J. Vermeer PDF
Proc. Amer. Math. Soc. 87 (1983), 533-535 Request permission

Abstract:

We show that not every semiregular space is embeddable as an open and dense set of some minimal Hausdorff space. Also a space is constructed for which it is not decidable in Z.F.C whether such an embedding exists.
References
  • S. Iliadis, Absolutes of Hausdorff spaces, Dokl. Akad. Nauk SSSR 149 (1963), 22–25 (Russian). MR 0157354
  • Miroslav Katětov, On $H$ closed extensions of topological spaces, Časopis Pěst. Mat. Fys. 72 (1947), 17–32 (English, with Czech summary). MR 0022069
  • Johannes Vermeer, Minimal Hausdorff and compactlike spaces, Topological structures, II (Proc. Sympos. Topology and Geom., Amsterdam, 1978) Math. Centre Tracts, vol. 116, Math. Centrum, Amsterdam, 1979, pp. 271–283. MR 565847
  • J. Vermeer and E. Wattel, Projective elements in categories with perfect $\theta$-continuous maps, Canad. J. Math. 4 (1981), 872-884.
  • R. Grant Woods, A survey of absolutes of topological spaces, Topological structures, II (Proc. Sympos. Topology and Geom., Amsterdam, 1978) Math. Centre Tracts, vol. 116, Math. Centrum, Amsterdam, 1979, pp. 323–362. MR 565852
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 87 (1983), 533-535
  • MSC: Primary 54D25; Secondary 03E35, 54A35, 54C25, 54G20
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0684652-7
  • MathSciNet review: 684652