Corollary 5

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

Topological Vector Spaces, chapter III, § 1. Bornology in a topological vector space

Let $E$ and $F$ be two locally convex spaces and $u : E \to F$ be a continuous polynomial mapping. If $A$ is a bounded subset of $E$ , then $u(A)$ is bounded.

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

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