- #1
CornMuffin
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Homework Statement
Prove:
If ##X## is a (possibly infinite dimensional) locally convex space, ##L \leq X##, ##dimL < \infty ##, and ##M \leq X ## then ##L + M## is closed.
Homework Equations
The Attempt at a Solution
##dimL < \infty \implies L## is closed in ##X##
##L+M = \{ x+y : x\in L, y \in M \} \implies ^{??} dim(L+M) < \infty \implies L+M ## is closed in ##X##