Lower continuous topological groups – A generalization of minimal groups

For two topological group topologies and on a certain group , we call is a predecessor of if is strictly coarser than and there is no other group topologies between them. A Hausdorff topological group is called lower continuous if its topology admits no Hausdorff predecessor. Evidently, minimal groups are lower continuous. Several elementary properties of this class of groups are also given in this talk.