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Proceedings of the American Mathematical Society

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

 

 

Spaces with given homeomorphism groups


Author: M. C. Thornton
Journal: Proc. Amer. Math. Soc. 33 (1972), 127-131
MSC: Primary 57E05
DOI: https://doi.org/10.1090/S0002-9939-1972-0292054-3
MathSciNet review: 0292054
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Abstract: A topological space X is constructed so that its group of homeomorphisms is isomorphic to a given finitely generated group G. If G has r generators and finite order n, X has $ n(2r + 1)$ points. The relation of X to certain covering spaces is considered.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0292054-3
Keywords: Finite topological space, A-space, homeomorphism groups, transformation groups, covering spaces, covering transformations
Article copyright: © Copyright 1972 American Mathematical Society