We know that if $G$ is a topological group and $C \subseteq G$ is compact and $A \subseteq G$ is closed, then $AC$ , $CA$ are closed.
Is it right to say:
The product of two closed subgroups in topological groups is closed?
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This is false: sum of two closed subspaces of a Banach space need not be closed.
Tomasz Kania
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do you have an example in topological group? i didn't get it. thanks. – Jun 14 '17 at 13:42
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1@adin, closed subspaces of a Banach space are subgroups of the topological group that is the Banach space – Maxime Ramzi Jun 14 '17 at 13:52