Function algebras and the lattice of compactifications
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- by Franklin Mendivil PDF
- Proc. Amer. Math. Soc. 127 (1999), 1863-1871 Request permission
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.References
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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
- MR Author ID: 610124
- Email: mendivil@augusta.math.uwaterloo.ca, mendivil@math.gatech.edu
- 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
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1863-1871
- MSC (1991): Primary 54D35, 54C35, 54D40, 46E25
- DOI: https://doi.org/10.1090/S0002-9939-99-04757-7
- MathSciNet review: 1487330