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

 

Local connectedness in transformation groups


Author: Keith Whittington
Journal: Proc. Amer. Math. Soc. 130 (2002), 903-907
MSC (2000): Primary 54H15; Secondary 54D05
Published electronically: July 31, 2001
MathSciNet review: 1866047
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Abstract: This note shows that under very general conditions, in a topological transformation group, the natural map from the group onto an orbit is almost open. The implications for local connectedness are investigated. In particular, if the image of a path component of the group is sufficiently ``robust", the orbit will be locally connected.


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Additional Information

Keith Whittington
Affiliation: Department of Mathematics, University of the Pacific, Stockton, California 95211
Email: kwhittin@uop.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06131-7
PII: S 0002-9939(01)06131-7
Received by editor(s): April 12, 2000
Received by editor(s) in revised form: August 28, 2000
Published electronically: July 31, 2001
Communicated by: Alan Dow
Article copyright: © Copyright 2001 American Mathematical Society