Vol. 43, No. 1, 1972

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
Volume:
Issue:
     
The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
Officers
 
Subscriptions
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
 
Special Issues
Author index
To appear
 
Other MSP journals
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