Local connectedness in transformation groups

Whittington, Keith

doi:10.1090/S0002-9939-01-06131-7

Local connectedness in transformation groups
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Proc. Amer. Math. Soc. 130 (2002), 903-907 Request permission

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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