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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1971-0267559-0
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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DOI: https://doi.org/10.1090/S0002-9939-1971-0267559-0
Keywords: Metric space, transformation group, equicontinuity
Article copyright: © Copyright 1971 American Mathematical Society