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Transactions of the American Mathematical Society

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Supercompactness of compactifications and hyperspaces


Author: Murray G. Bell
Journal: Trans. Amer. Math. Soc. 281 (1984), 717-724
MSC: Primary 54D30; Secondary 54B20
DOI: https://doi.org/10.1090/S0002-9947-1984-0722770-0
MathSciNet review: 722770
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Abstract: We prove a theorem which implies that if $ \gamma \omega $ is a supercompact compactification of the countable discrete space $ \omega $ then $ \gamma \omega - \omega $ is separable. This improves an earlier result of the author's that such a $ \gamma \omega $ must have $ \gamma \omega - \omega \;{\text{ccc}}$. We prove a theorem which implies that the hyperspace of closed subsets of $ {2^{\omega_2}}$ is not a continuous image of a supercompact space. This improves an earlier result of $ {\text{L}}$. Šapiro that the hyperspace of closed subsets of $ {2^{\omega_2}}$ is not dyadic.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1984-0722770-0
Keywords: Supercompact, hyperspace, dyadic
Article copyright: © Copyright 1984 American Mathematical Society

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