Proposition 1

Tag 0790, permanent. Cite it as [Bourbaki, Tag 0790].

Topological Vector Spaces, chapter I, § 2. Linear varieties in a topological vector space

— In a topological vector space $E$ , the closure of a linear variety is a linear variety.

Since every translation is a homeomorphism of $E$ , it is sufficient to demonstrate the proposition for a vector subspace $M$ of $E$ , and in this case, the proposition has been proved in I, p. 4.

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

Cited by

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Cites

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