On low dimensional minimal sets

Soon-Kyu Kim

Vol. 43 (1972), No. 1, 171–174

DOI: 10.2140/pjm.1972.43.171

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 dim_L(X) ≦ 2 then X is a manifold, imposing a further condition on the action when dim_L(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