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A theorem on near equicontinuity of transformation groups

Author: Fred A. Roberson
Journal: Proc. Amer. Math. Soc. 27 (1971), 189-191
MSC: Primary 54.82
MathSciNet review: 0267559
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Abstract: A transformation group is nearly equicontinuous if the set of nonequicontinuous points is zero dimensional and compact. It has been shown that if a transformation group is nearly equicontinuous with locally compact, locally connected metric phase space and if the set of equicontinuous points is connected, then the set $ N$ of nonequicontinuous points can contain at most two minimal sets. In this paper we will show that if in addition the phase space is not compact, then $ N$ contains exactly one minimal set.

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Keywords: Metric space, transformation group, equicontinuity
Article copyright: © Copyright 1971 American Mathematical Society

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