Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
DOI: https://doi.org/10.1090/S0002-9939-05-07808-1
Published electronically: February 25, 2005
MathSciNet review: 2138866
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $G$.


References [Enhancements On Off] (What's this?)

  • 1. E. G. Effros, Transformation groups and $C^*$-algebras, Annals of Math. 81 (1965), 38-55. MR 0174987 (30:5175)
  • 2. L. R. Ford, Jr., Homeomorphism groups and coset spaces, Trans. Amer. Math. Soc. 77 (1954), 490-497. MR 0066636 (16:609a)
  • 3. M. G. Megrelishvili, A Tikhonov $G$-space admitting no compact Hausdorff $G$-extension or $G$-linearization, Russian Math. Surveys 43 (1988), 177-178. MR 0940673 (89e:54080)
  • 4. J. van Mill, The infinite-dimensional topology of function spaces, North-Holland Publishing Co., Amsterdam, 2001. MR 1851014 (2002h:57031)
  • 5. J. van Mill, A note on Ford's Example, 2003, to appear in Topology Proc.
  • 6. P. S. Mostert, Reasonable topologies for homeomorphism groups, Proc. Amer. Math. Soc. 12 (1961), 598-602. MR 0130681 (24:A541)
  • 7. G. S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-400. MR 0385825 (52:6684)
  • 8. V. V. Uspenskii, Topological groups and Dugundji compact spaces, Mat. Sb. 180 (1989), 1092-1118. MR 1019483 (91a:54064)
  • 9. J. de Vries, On the existence of $G$-compactifications, Bull. Polon. Acad. Sci. Sér. Math. Astronom. Phys. 26 (1978), 275-280. MR 0644661 (58:31002)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 20M20, 54H15

Retrieve articles in all journals with MSC (2000): 20M20, 54H15


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: https://doi.org/10.1090/S0002-9939-05-07808-1
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.

American Mathematical Society