Geodesic
Some Theorems on the Structure of Nearly Equicontinuous Transformation Groups
Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 421-425

Voir la notice de l'article provenant de la source Cambridge University Press

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.) 
Roberson, Fred A. Some Theorems on the Structure of Nearly Equicontinuous Transformation Groups. Canadian journal of mathematics, Tome 23 (1971) no. 3, pp. 421-425. doi: 10.4153/CJM-1971-044-x
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