Corollary

Tag 0BWA, permanent. Cite it as [Bourbaki, Tag 0BWA].

General Topology, chapter VI, § 1. Real number space R^n

The complement of an affine linear variety of dimension $p < n$ is dense in $\mathbf{R}^n$ .

Since every affine linear variety of dimension $p < n$ is contained in a hyperplane, it is enough to prove the corollary for a hyperplane; but a hyperplane is defined by an equation $g(x) = 0$ , where $g$ is a linear polynomial not identically zero.

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

Cited by

§ 3. Real projective spaces

Cites

Nothing.