Vol. 38, No. 2, 1971

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ISSN: 0030-8730
On completeness

Norman Ray Howes

Vol. 38 (1971), No. 2, 431–440
Abstract

Hisahiro Tamano asked the following question that motivated his Some properties of the Stone-Cech compactification, J. Math. Soc. Japan, vol. 12, 1 (1960) 104–117. “What is a necessary and sufficient condition for a uniform space to have a paracompact completion?”. Although he did not arrive at a solution, he obtained characterizations of completeness, paracompactness, and the structure of the completion of a uniform space by means of the radical.

This paper provides an answer to the above question and related ones. Also included is a development of other types of completeness in both uniform and non-uniform topological spaces. These other “complete” spaces yield characterizations of paracompactness and the Lindelöf property as well as necessary and sufficient conditions for paracompact spaces to be Lindelöf and entirely normal spaces to be paracompact.

Mathematical Subject Classification 2000
Primary: 54E15
Secondary: 54D20
Milestones
Received: 2 March 1970
Revised: 27 September 1970
Published: 1 August 1971
Authors
Norman Ray Howes