I have a simple question:
Let $A$, $B$ be closed subspaces of banach space $X$ and $B\subseteq A$, if $\dim A/B<\infty$ and $\dim B<\infty$, then $\dim A<\infty$? Why?
2026-04-06 04:55:18.1775451318
A simple question about the dimension of subspace.
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This happens just because they are vector spaces. A set of generators for $A$ can be obtained by adding to a (finite) set of generators of $B$ a (finite) set of representants for the generators of $A/B$.