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Spaces having no large dyadic subspace

Published online by Cambridge University Press:  17 April 2009

Jason Gait
Jason Gait
Affiliation:
Wesleyan University, Middletown, Connecticut, USA.
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Abstract

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Gillman-Henriksen have defined a class of spaces, containing the discrete spaces and their Stone-Čech compactifications, called F'-spaces. The dyadic spaces are the continuous images of products of finite discrete spaces – a class which contains the compact metric spaces and all compact topological groups. In this paper it is shown that F'-spaces have no infinite dyadic sutspaces and, almost always, no dyadic compactifications. An interesting corollary is that if βX \ X is dyadic, then X is pseudocompact.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 2 , Issue 2 , April 1970 , pp. 261 - 265
Copyright
Copyright © Australian Mathematical Society 1970

References

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