Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] B. Clark and V. Schneider, The normal extensions of subgroup topologies, Proc. Amer. Math. Soc. 97 (1986), 163-166. MR 831407 (87d:22002)
  • [2] M. Lamper, Complements in the lattice of all topologies of topological groups, Arch. Math. (Brunensis) 4 (1974), 221-230. MR 0401977 (53:5800)
  • [3] D. Remus, Zur Struktur des Verbandes der Gruppentopologien, Dissertation, Universität Hannover, 1983.
  • [4] P. Samuel, Ultrafilters and compactifications of uniform spaces, Trans. Amer. Math. Soc. 64 (1948), 100-134. MR 0025717 (10:54a)
  • [5] S. Willard, General topology, Addison-Wesley, Reading, Mass., 1970. MR 0264581 (41:9173)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 22A05, 54H99

Retrieve articles in all journals with MSC: 22A05, 54H99

Additional Information

Article copyright: © Copyright 1986 American Mathematical Society

American Mathematical Society