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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Relationship between the meet and join operators in the lattice of group topologies


Authors: Bradd Clark and Victor Schneider
Journal: Proc. Amer. Math. Soc. 98 (1986), 681-682
MSC: Primary 22A05; Secondary 54H99
MathSciNet review: 861775
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Abstract: Let $ L(G)$ be the lattice of all topologies on the group $ G$ which make $ G$ into a topological group. If $ {\tau _1}$ and $ {\tau _2}$ are Hausdorff group topologies and $ {\tau _1} \vee {\tau _2}$ is the discrete topology, then $ {\tau _1} \wedge {\tau _2}$ is a Hausdorff topology. If $ {\tau _1}$ and $ {\tau _2}$ are locally compact Hausdorff group topologies, then $ {\tau _1} \vee {\tau _2}$ is locally compact if and only if $ {\tau _1} \wedge {\tau _2}$ is Hausdorff.


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DOI: https://doi.org/10.1090/S0002-9939-1986-0861775-3
Article copyright: © Copyright 1986 American Mathematical Society