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Some Theorems on the Structure of Nearly Equicontinuous Transformation Groups

Published online by Cambridge University Press:  20 November 2018

Fred A. Roberson
Fred A. Roberson*
Affiliation:
The Florida State University, Tallahassee, Florida
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The purpose of this paper is to extend the theorems in [3; 7] to uniform spaces and to prove some additional theorems. These results are related to [4; 5]. Notation and definitions are as in the book [2]. For a general reference on nets see [6]. All topological spaces are assumed to be Hausdorff.

THEOREM 1. Let (X, T, Π) be a transformation group, where X is a locally compact, locally connected, uniform space. Let E denote the set of all points at which T is equicontinuous and N = X – E. Let N be closed totally disconnected and each orbit closure in N be compact and let E be connected. Then N contains at most two minimal sets. (Note: We will assume that N ≠ ∅ so that N will contain at least one minimal set.)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 23 , Issue 3 , June 1971 , pp. 421 - 425
Copyright
Copyright © Canadian Mathematical Society 1971

References

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