When is the Sum of Two Closed Subgroups Closed in a Locally Compact Abelian Group

Wolfgang Herfort; Karl H. Hofmann; Francesco G. Russo

doi:10.1016/j.topol.2019.106958

paper

When is the Sum of Two Closed Subgroups Closed in a Locally Compact Abelian Group

arXiv:1908.08420 · doi:10.1016/j.topol.2019.106958

Abstract

Locally compact abelian groups are classified in which the sum of any two closed subgroups is itself closed. This amounts to reproving and extending results by Yu.~N.~Mukhin from 1970. Namely we contribute a complete classification of all totally disconnected \lca\ groups with $X + Y$ closed for any closed subgroups $X$ and $Y$ .

38 pages, 1 figure