Vol. 29, No. 1, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Critical points on rim-compact spaces

David Hilding Carlson

Vol. 29 (1969), No. 1, 63–65
Abstract

In this note we prove that all the points of a rim-compact space X at which X is not locally compact are critical points for any local dynamical system defined on X. When a local system is global this result is obtained by extending the global system π on X to a global system ρ on the Freudenthal compactification Y of X, then showing that Y X is a critical set for ρ, and, finally, observing that Y X contains all the points of X at which X is not locally compact. This weaker result will appear in the author’s doctoral dissertation and requires the use of general extension theorems proven there. For this paper, we isolate those parts of the thesis which are pertinent to our theorem.

Mathematical Subject Classification
Primary: 54.82
Milestones
Received: 1 July 1968
Published: 1 April 1969
Authors
David Hilding Carlson