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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Nonhomogeneity of products of preimages and $ \pi $-weight


Author: Eric K. van Douwen
Journal: Proc. Amer. Math. Soc. 69 (1978), 183-192
MSC: Primary 54F99; Secondary 54A25
DOI: https://doi.org/10.1090/S0002-9939-1978-0644652-8
MathSciNet review: 0644652
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Abstract: We prove a general nonhomogeneity result which implies among others

(1) if X is a homogeneous Hausdorff space, then $ \vert X\vert \leqslant {2^{\pi (X)}}$;

(2) no power of $ \beta (\omega ) - \omega $, or of $ \beta Q - Q$ or of $ \beta R - R$ is homogeneous.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0644652-8
Keywords: Nonhomogeneity, $ \pi $-weight, product, preimage, way to cluster
Article copyright: © Copyright 1978 American Mathematical Society