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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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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There can be $C^ *$-embedded dense proper subspaces in $\beta \omega -\omega$
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by Eric K. van Douwen, Kenneth Kunen and Jan van Mill
Proc. Amer. Math. Soc. 105 (1989), 462-470
DOI: https://doi.org/10.1090/S0002-9939-1989-0977925-7

Abstract:

Fine and Gillman have shown that CH implies that if $X$ is a dense proper subspace of ${\omega ^ * } = \beta \omega - \omega$, then $\beta X \ne {\omega ^ * }$. Here it is shown to be consistent with ${\text {MA + c = }}{\omega _2}$ that for every $p \in {\omega ^ * }$ we have $\beta ({\omega ^ * } - \{ p\} ) = {\omega ^ * }$ and also that ${\omega ^ * }$ has a dense subspace $X$ with dense complement such that $\beta X = {\omega ^ * }$.
References
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 105 (1989), 462-470
  • MSC: Primary 54D35; Secondary 03E35, 54A35
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0977925-7
  • MathSciNet review: 977925