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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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finite codimension implies closed?

Let $E$ be a (complete) topological vector space, and $u:E\to E$ be continuous. Is it always true that if ${\rm Im}(u)$ is of finite codimension in $E$, then it is closed in $E$ or do we have to assu …
Guy Relande's user avatar