Vol. 43, No. 1, 1972

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On low dimensional minimal sets

Soon-Kyu Kim

Vol. 43 (1972), No. 1, 171–174
Abstract

Let (X,G,f) be a topological transformation group. Suppose that the phase space X is compact, separable metric, and locally contractible and the group G is the additive group of all real numbers R with the usual topology. If X is a minimal set of dimL(X) 2 then X is a manifold, imposing a further condition on the action when dimL(X) = 2. Hence X is a singleton, a circle or a torus according to its dimension.

Mathematical Subject Classification 2000
Primary: 54H20
Milestones
Received: 27 May 1971
Revised: 26 July 1971
Published: 1 October 1972
Authors
Soon-Kyu Kim