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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

[1]Corson, H.H., “Normality in subsets of product spaces”, Amer. J. Math. 81 (1959), 785–796.Google Scholar
[2]Efimov, B. and Engelking, R., “Remarks on dyadic spaces II”, Colloq. Math. 13 (1965), 181–197.Google Scholar
[3]Efimov, B.; “Dyadic bicompacta”, Soviet Math. Dokl. 4 (1963), 496–500.Google Scholar
[4]Engelking, R. and Pelczynski, A., “Remarks on dyadic spaces”, Colloq. Math. 11 (1963), 55–63.Google Scholar
[5]Gillman, Leonard and Henriksen, Melvin, “Rings of continuous functions in which every finitely generated ideal is principal”, Trans. Amer. Math. Soc. 82 (1956), 366–391.Google Scholar
[6]Gillman, Leonard and Jerison, Meyer, Rings of continuous functions (Van Nostrand, Princeton, New Jersey, 1960).Google Scholar