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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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A symmetrizable space that is not perfect
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by Dennis A. Bonnett PDF
Proc. Amer. Math. Soc. 34 (1972), 560-564 Request permission

Abstract:

An example is given of a Hausdorff symmetrizable space which has a closed subset that is not a ${G_\delta }$-subset (thus, it is not perfect) and which is not subparacompact. This example is then used in the construction of a symmetrizable ${T_1}$-space Y having a point ${x_0}$ such that $\{ {x_0}\}$ is not a ${G_\delta }$-subset of Y.
References
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Additional Information
  • © Copyright 1972 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 34 (1972), 560-564
  • MSC: Primary 54A25
  • DOI: https://doi.org/10.1090/S0002-9939-1972-0295275-9
  • MathSciNet review: 0295275