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The completion of a topological group

Published online by Cambridge University Press:  17 April 2009

Eric C. Nummela
Eric C. Nummela
Affiliation:
Department of Mathematics, New England College, Henniker, New Hampshire 03242, USA.
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During the 1920's and 30's, two distinct theories of “completions” for topological spaces were being developed: the French school of mathematics was describing the familiar notion of “complete relative to a uniformity”, and the Russian school the less well-known idea of “absolutely closed”. The two agree precisely for compact spaces.

The first part of this article describes these two notions of completeness; the remainder is a presentation of the interesting, but apparently unrecorded, fact that the two ideas coincide when put in the context of topological groups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 3 , June 1980 , pp. 407 - 417
Copyright
Copyright © Australian Mathematical Society 1980

References

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