Corollary

Tag 07EZ, permanent. Cite it as [Bourbaki, Tag 07EZ].

Topological Vector Spaces, II, p. 35, § 4. Locally convex spaces

If $L$ is a compact set in $F$ , then there exists a compact set $K$ in $E$ such that $u(K) = L$ .

It is sufficient to put $K = s(L)$ , where $s$ is a continuous section of $u$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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