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arXiv · 1908.08420

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

Wolfgang Herfort·Karl H. Hofmann·Francesco G. Russo
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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 $Y$.

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Wolfgang Herfort, Karl H. Hofmann, Francesco G. Russo. 2019-08-22. When is the Sum of Two Closed Subgroups Closed in a Locally Compact Abelian Group. https://doi.org/10.1016/j.topol.2019.106958

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