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Proceedings of the American Mathematical Society

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

 

 

A rigid space $ X$ for which $ X\times X$ is homogeneous; an application of infinite-dimensional topology


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 83 (1981), 597-600
MSC: Primary 54G15; Secondary 57N20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627701-2
MathSciNet review: 627701
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Abstract: We give an example of a rigid (= no autohomeomorphisms beyond the identity) space $ X$ such that $ X \times X$ is homogeneous. In fact, $ X \times X$ is homeomorphic to the Hilbert cube. This answers a question of A. V. Arhangel'skiĭ.


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DOI: https://doi.org/10.1090/S0002-9939-1981-0627701-2
Article copyright: © Copyright 1981 American Mathematical Society