Lower continuous topological groups (Q2324550)

In this paper, the following results are proved: 1) A Hausdorff topological group is minimal if and only if it is locally minimal and lower continuous. 2) A closed central subgroup of a lower continuous group is lower continuous. In particular, every closed subgroup of a lower continuous topological abelian group is lower continuous. 3) A torsion-free Hausdorff topological abelian group is lower continuous if and only if all its subgroups are lower continuous. 4) Every topological product of a family of minimal abelian groups is lower continuous. 5) A closed central subgroup of a totally lower continuous group is totally lower continuous. 6) A minimal totally lower continuous abelian group is totally minimal. 7) Every totally lower continuous abelian group is precompact. 8) A compact abelian group is hereditarily lower continuous if and only if it is torsion-free.