Vol. 51, No. 2, 1974

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
Subscriptions
Editorial Board
Officers
Contacts
 
Submission Guidelines
Submission Form
Policies for Authors
 
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author Index
To Appear
 
Other MSP Journals
Regular completions of Cauchy spaces

Darrell Conley Kent and Gary Douglas Richardson

Vol. 51 (1974), No. 2, 483–490
Abstract

A uniform convergence space is a generalization of a uniform space. The set of all Cauchy filters of some uniform convergence space is called a Cauchy structure. We give necessary and sufficient conditions for the Cauchy structure of some totally bounded uniform convergence space to be precompact; i.e., have a regular completion. Also, it is shown that there is an isomorphism between the set of ordered equivalence classes of strict regular compactifications of a completely regular convergence space and the set of ordered precompact Cauchy structures inducing the given convergence structure.

Mathematical Subject Classification 2000
Primary: 54A20
Secondary: 54D35
Milestones
Received: 29 November 1972
Revised: 22 August 1973
Published: 1 April 1974
Authors
Darrell Conley Kent
Gary Douglas Richardson