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
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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