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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Function algebras and the lattice
of compactifications


Author: Franklin Mendivil
Journal: Proc. Amer. Math. Soc. 127 (1999), 1863-1871
MSC (1991): Primary 54D35, 54C35, 54D40, 46E25
Published electronically: February 17, 1999
MathSciNet review: 1487330
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Abstract | References | Similar Articles | Additional Information

Abstract: We provide some conditions as to when $K(X) \cong K(Y)$ for two locally compact spaces $X$ and $Y$ (where $K(X)$ is the lattice of all Hausdorff compactifications of $X$). More specifically, we prove that $K(X) \cong K(Y)$ if and only if $C^*(X)/C_0(X) \cong C^*(Y)/C_0(Y)$. Using this result, we prove several extensions to the case where $K(X)$ is embedded as a sub-lattice of $K(Y)$ and to where $X$ and $Y$ are not locally compact.

One major contribution is in the use of function algebra techniques. The use of these techniques makes the extensions simple and clean and brings new tools to the subject.


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Additional Information

Franklin Mendivil
Affiliation: Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Address at time of publication: Department of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332-0160
Email: mendivil@augusta.math.uwaterloo.ca, mendivil@math.gatech.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04757-7
PII: S 0002-9939(99)04757-7
Keywords: Function algebras, compactifications, lattice of compactifications, maximal ideals, structure space, rings of continuous functions
Received by editor(s): December 10, 1996
Received by editor(s) in revised form: September 22, 1997
Published electronically: February 17, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society