A Compactification due to Fell
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 145-146
Voir la notice de l'article provenant de la source Cambridge University Press
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 T 0 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.
Wulfsohn, Aubrey. A Compactification due to Fell. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 145-146. doi: 10.4153/CMB-1972-028-3
@article{10_4153_CMB_1972_028_3,
author = {Wulfsohn, Aubrey},
title = {A {Compactification} due to {Fell}},
journal = {Canadian mathematical bulletin},
pages = {145--146},
year = {1972},
volume = {15},
number = {1},
doi = {10.4153/CMB-1972-028-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-028-3/}
}
[1] 1. Bourbaki, N., Topologie générale, Ch. I, Hermann, Paris, 1965. Google Scholar
[2] 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] 3. Fell, J. M. G., The structure of operator algebra fields, Acta Math. 106 (1961), 233-280. Google Scholar
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