A short proof of a cardinal inequality involving homogeneous spaces

Frankiewicz, Ryszard

doi:10.1090/S0002-9939-1979-0532168-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A short proof of a cardinal inequality involving homogeneous spaces
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by Ryszard Frankiewicz PDF

Proc. Amer. Math. Soc. 75 (1979), 372-373 Request permission

Abstract:

We give a short proof of van Douwen’s theorem that $|X| \leqslant {2^{\pi (X)}}$ holds for homogeneous Hausdorff spaces.

References

Eric K. van Douwen, Nonhomogeneity of products of preimages and $\pi$-weight, Proc. Amer. Math. Soc. 69 (1978), no. 1, 183–192. MR 644652, DOI 10.1090/S0002-9939-1978-0644652-8
I. Juhász, Cardinal functions in topology, Mathematical Centre Tracts, No. 34, Mathematisch Centrum, Amsterdam, 1971. In collaboration with A. Verbeek and N. S. Kroonenberg. MR 0340021