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Compactifications and quotient lattices of Wallman bases

Published online by Cambridge University Press:  17 April 2009

Eliza Wajch
Eliza Wajch
Affiliation:
Institute of Mathematics, University of Łódź, S. Banacha 22, 90-238 Łódź, Poland, e-mail: ewajch@krysia.uni.lodz.pl
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Abstract

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We improve the intuition and some ideas of G. D. Faulkner and M. C. Vipera presented in the article “Remainders of compactifications and their relation to a quotient lattice of the topology” [Proc. Amer. Math. Soc. 122 (1994)] in connection with the question about internal conditions for locally compact spaces X and Y under which βX/X ≅ βY/Y or, more generally, under which the remainders of compactifications of X belong to the collection of the remainders of compactifications of Y. We point out the reason why the quotient lattice of the topology considered by Faulkner and Vipera cannot lead to a satisfactory answer to the above question. We replace their lattice by the qoutient lattice of a new equivalence relation on a Wallman base in order to describe a method of constructing a Wallman-type compactification which allows us to deduce more complete solutions to the problems investigated by Faulkner and Vipera.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 54 , Issue 1 , August 1996 , pp. 115 - 130
Copyright
Copyright © Australian Mathematical Society 1996

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