Vol. 113, No. 1, 1984

Recent Issues
Vol. 284: 1
Vol. 283: 1  2
Vol. 282: 1  2
Vol. 281: 1  2
Vol. 280: 1  2
Vol. 279: 1
Vol. 278: 1  2
Vol. 277: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Subscriptions
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Completeness in semimetric spaces

Fred Galvin and Samuel David Shore

Vol. 113 (1984), No. 1, 67–75
Abstract

We establish interrelationships between Cauchy completeness, McAuley’s notions of strong and weak completeness, and Moore completeness in semimetrizable spaces as well as developable, 1-continuously, or continuously semimetrizable spaces.

Our main result shows that a semimetrizable space may admit one semimetric which is Cauchy complete and a second semimetric which is developable, and yet will not admit a semimetric which is simultaneously Cauchy complete and developable.

Mathematical Subject Classification 2000
Primary: 54E25
Secondary: 54E30
Milestones
Received: 12 April 1982
Revised: 12 May 1983
Published: 1 July 1984
Authors
Fred Galvin
Samuel David Shore