Vol. 94, No. 2, 1981

Recent Issues
Vol. 329: 1
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
A note on regular Cauchy spaces

Darrell Conley Kent

Vol. 94 (1981), No. 2, 333–339
Abstract

A regular convergence space has both a finest and coarsest compatible regular Cauchy structure. The coarsest compatible regular Cauchy structure is complete if and only if the original space is Urysohn-closed; it is totally bounded if and only if the original space is almost topological. Minimal regular Cauchy spaces are characterized and, in the complete case, shown to be in one-to-one correspondence with the minimal regular convergence spaces. The noncomplete minimal regular regular Cauchy spaces do not have regular completions.

Mathematical Subject Classification 2000
Primary: 54A20
Milestones
Received: 1 December 1978
Published: 1 June 1981
Authors
Darrell Conley Kent