Geodesic
The Meet Operator in the Lattice of Group Topologies
Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 478-481

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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.
DOI : 10.4153/CMB-1986-075-x
Mots-clés : 22A05 
Clark, Bradd; Schneider, Victor. The Meet Operator in the Lattice of Group Topologies. Canadian mathematical bulletin, Tome 29 (1986) no. 4, pp. 478-481. doi: 10.4153/CMB-1986-075-x
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     title = {The {Meet} {Operator} in the {Lattice} of {Group} {Topologies}},
     journal = {Canadian mathematical bulletin},
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     year = {1986},
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     number = {4},
     doi = {10.4153/CMB-1986-075-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-075-x/}
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