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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Strong local homogeneity and coset spaces


Author: Jan van Mill
Journal: Proc. Amer. Math. Soc. 133 (2005), 2243-2249
MSC (2000): Primary 20M20, 54H15
Published electronically: February 25, 2005
MathSciNet review: 2138866
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Abstract: We prove that for every homogeneous and strongly locally homogeneous separable metrizable space $X$ there is a metrizable compactification $\gamma X$ of $X$ such that, among other things, for all $x,y\in X$ there is a homeomorphism $f\colon\gamma X\to \gamma X$ such that $f(x)=y$. This implies that $X$ is a coset space of some separable metrizable topological group $G$.


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Additional Information

Jan van Mill
Affiliation: Department of Mathematics, Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081$^{a}$, 1081 HV Amsterdam, The Netherlands
Email: vanmill@cs.vu.nl

DOI: http://dx.doi.org/10.1090/S0002-9939-05-07808-1
PII: S 0002-9939(05)07808-1
Keywords: Topological group, action, coset space, strongly locally homogeneous
Received by editor(s): January 31, 2004
Received by editor(s) in revised form: April 13, 2004
Published electronically: February 25, 2005
Communicated by: Alan Dow
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.