Abstract
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].
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