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Relations between Non-Compact Transformation Groups and Compact Transformation Groups

Published online by Cambridge University Press:  22 January 2016

Hsin Chu
Hsin Chu*
Affiliation:
University of Maryland
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In this paper certain relations between non-compact transformation groups and compact transformation groups are studied. The notion of re-ducibility and separability of transformation groups is introduced, several necessary and sufficient conditions are established: (1) A separable transformation group to be locally weakly almost periodic, (2) A reducible and separable transformation group to be a minimal set and (3) A reducible and separable transformation group to be a fibre bundle. As applications we show, among other things, that (1) for certain reducible transformation groups its fundamental group is not trivial which is a generalization of a result in [4].

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 44 , December 1971 , pp. 97 - 117
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1971

References

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