Vol. 38, No. 2, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 329: 1  2
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
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
On completeness

Norman Ray Howes

Vol. 38 (1971), No. 2, 431–440

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
Received: 2 March 1970
Revised: 27 September 1970
Published: 1 August 1971
Norman Ray Howes