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Proceedings of the American Mathematical Society

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

 
 

 

Homeomorphism groups and homogeneous spaces


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 92 (1984), 449-454
MSC: Primary 54C35; Secondary 54F20, 54H10
DOI: https://doi.org/10.1090/S0002-9939-1984-0759672-5
MathSciNet review: 759672
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Abstract: We show that the $ 2$-sphere $ {S^2}$ can be decomposed into two sets $ A$ and $ B$ such that (1) both $ A$ and $ B$ are connected, locally connected, dense and Baire, (2) both $ A$ and $ B$ are (much more than) topologically homogeneous, (3) $ A$ is not homeomorphic to $ B$, and (4) the autohomeomorphism groups of $ A$ and $ B$ are (algebraically) isomorphic.


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DOI: https://doi.org/10.1090/S0002-9939-1984-0759672-5
Article copyright: © Copyright 1984 American Mathematical Society

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