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Local connectedness in transformation groups

Author(s): Keith Whittington
Journal: Proc. Amer. Math. Soc. 130 (2002), 903-907.
MSC (2000): Primary 54H15; Secondary 54D05
Posted: July 31, 2001
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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.

References:

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3.: E. Hewitt and K. Ross, Abstract Harmonic Analysis, Vol. I, second ed., Springer-Verlag, 1979 New York. MR 81k:43001
4.: G. S. Ungar, On all kinds of homogeneous spaces, Trans. Amer. Math. Soc. 212 (1975), 393-400. MR 52:6684
5.: K. Whittington, A generalization of 2-homogeneous continua being locally connected, Proc. Amer. Math. Soc. 126 No. 10 (1998), 3131-3132. MR 99a:54024


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