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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $ C\sp \ast$-embedding in $ \beta {\bf N}$ and the continuum hypothesis


Authors: Alan S. Dow and R. Grant Woods
Journal: Proc. Amer. Math. Soc. 93 (1985), 549-554
MSC: Primary 54C45; Secondary 03E50, 54A35, 54D35
MathSciNet review: 774021
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Abstract: Let $ \beta {\mathbf{N}}$ denote the Stone-Čech compactification of the natural numbers $ {\mathbf{N}}$ with the discrete topology. It is shown that the continuum hypothesis holds iff for each pair $ X$ and $ Y$ of homeomorphic subspaces of $ \beta {\mathbf{N}}$, $ X$ is $ {C^*}$-embedded in $ \beta {\mathbf{N}}$ iff $ Y$ is. Related questions concerning $ {C^*}$-embedded subsets of $ \beta {\mathbf{N}}$ are investigated assuming the hypothesis $ {2^{{\aleph _0}}} < {2^{{\aleph _1}}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1985-0774021-5
PII: S 0002-9939(1985)0774021-5
Keywords: $ {C^*}$-embedding in $ \beta {\mathbf{N}}$
Article copyright: © Copyright 1985 American Mathematical Society