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The Meet Operator in the Lattice of Group Topologies

Published online by Cambridge University Press:  20 November 2018

Bradd Clark  and
Victor Schneider
Bradd Clark
Affiliation:
Dept. of Mathematics & Statistics University of Southern Louisiana Lafayette, LA 70504, U.S.A.
Victor Schneider
Affiliation:
Dept. of Mathematics & Statistics University of Southern Louisiana Lafayette, LA 70504, U.S.A.
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Abstract

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It is well known that the lattice of topologies on a set forms a complete complemented lattice. The set of topologies which make G into a topological group form a complete lattice L(G) which is not a sublattice of the lattice of all topologies on G.

Let G be an infinite abelian group. No nontrivial Hausdorff topology in L(G) has a complement in L(G). If τ1 and τ2 are locally compact topologies then τ1Λτ2 is also a locally compact group topology. The situation when G is nonabelian is also considered.

Keywords

22A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 4 , 01 December 1986 , pp. 478 - 481
Copyright
Copyright © Canadian Mathematical Society 1986

References

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