Relationship between the meet and join operators in the lattice of group topologies
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- by Bradd Clark and Victor Schneider PDF
- Proc. Amer. Math. Soc. 98 (1986), 681-682 Request permission
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.References
- Bradd Clark and Victor Schneider, The normal extensions of subgroup topologies, Proc. Amer. Math. Soc. 97 (1986), no. 1, 163–166. MR 831407, DOI 10.1090/S0002-9939-1986-0831407-9
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Additional Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 98 (1986), 681-682
- MSC: Primary 22A05; Secondary 54H99
- DOI: https://doi.org/10.1090/S0002-9939-1986-0861775-3
- MathSciNet review: 861775