Completeness of the factor group of a complete topological group and completeness of the factor ring of a complete topological ring by a compact normal subgroup and a compact ideal, respectively [Articol]

Abstract

If M is a subgroup of an Abelian group G(+) and τ is a group topology on the group G such that (G, τ ) is a complete topological group and M is a compact or it is locally compact subgroup of the topological group (G, τ ), then the factor group (G, τ ) = (G, τ )/M is a complete topological group.