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A Compactification due to Fell

Published online by Cambridge University Press:  20 November 2018

Aubrey Wulfsohn
Aubrey Wulfsohn*
Affiliation:
Centre De Recherches Mathématiques, Université De Montréal, Montréal, Québec
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We give an alternative construction of a Hausdorff compactification due to Fell [2]. We say that a space is compact if it has the Heine-Borel property, locally compact if each point has a fundamental system of compact neighbourhoods. The interesting spaces from the point of view of this paper, are the non-Hausdorjf ones since for locally compact Hausdorff spaces Fell's compactification is the usual one-point compactification. The motivation for the compactification comes from the theory of continuous fields of C*-algebras: the primitive spectrum of a C*- algebra A is a locally compact T0 space X and Fell [3] realizes A as an algebra of fields of operators over the compactification of X. This note is based on a discussion of the author with Professor Fell.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 1 , March 1972 , pp. 145 - 146
Copyright
Copyright © Canadian Mathematical Society 1972

References

1. Bourbaki, N., Topologie générale, Ch. I, Hermann, Paris, 1965.Google Scholar
2. Fell, J. M. G., A Hausdorff topology for the closed subsets of a locally compact non-Hausdorff space, Proc. Amer. Math. Soc. 13 (1962), 472-476.Google Scholar
3. Fell, J. M. G., The structure of operator algebra fields, Acta Math. 106 (1961), 233-280.Google Scholar