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

 

A class of maximal ideals in the lattice of topologies


Authors: W. J. Thron and R. A. Valent
Journal: Proc. Amer. Math. Soc. 87 (1983), 330-334
MSC: Primary 54A10; Secondary 06B10
MathSciNet review: 681843
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Abstract: In this article we investigate maximal ideals in the lattice of all topologies on a fixed set. Padmanabhan and Rao were the first to study maximal ideals in this lattice. They characterized the principal maximal ideals. Their main result was incorrect but their approach proved helpful to us. We exhibit a class of nonprincipal maximal ideals and also give an example to show that the class in question is not exhaustive.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0681843-6
PII: S 0002-9939(1983)0681843-6
Article copyright: © Copyright 1983 American Mathematical Society