Vol. 113, No. 1, 1984

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ISSN: 0030-8730
Completeness in semimetric spaces

Fred Galvin and Samuel David Shore

Vol. 113 (1984), No. 1, 67–75
DOI: 10.2140/pjm.1984.113.67
Abstract
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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