Vol. 35, No. 2, 1970

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 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
A conditionally compact point set with noncompact closure

David Edwin Cook

Vol. 35 (1970), No. 2, 313–319
Abstract

Sometime in 1930, Leo Zippin showed that there exists a complete Moore space that contains a conditionally compact point set whose closure is not compact. It is the object of this paper to show that if the hypothesis of the continuum is true then there exists a separable, complete Moore space wkick contains such a point set and, furthermore, satisfies R. L. Moore’s Axioms 2, 3, 4, 5, and 6. Theorem 1, concerning the existemce of certain subsets of the Cartesian plane, is fundamental to the construction of this example and its proof constitutes a major portion of this paper.

Mathematical Subject Classification
Primary: 54.38
Milestones
Received: 18 December 1969
Published: 1 November 1970
Authors
David Edwin Cook