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

DOI:
https://doi.org/10.1090/S0002-9939-99-04757-7

Published electronically:
February 17, 1999

MathSciNet review:
1487330

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We provide some conditions as to when for two locally compact spaces and (where is the lattice of all Hausdorff compactifications of ). More specifically, we prove that if and only if . Using this result, we prove several extensions to the case where is embedded as a sub-lattice of and to where and 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:
https://doi.org/10.1090/S0002-9939-99-04757-7

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