Affine and homeomorphic embeddings into ℓ²

Bessaga, Czesław; Dobrowolski, Tadeusz

doi:10.1090/S0002-9939-97-03832-X

Affine and homeomorphic embeddings into $\ell ^2$
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by Czesław Bessaga and Tadeusz Dobrowolski PDF

Proc. Amer. Math. Soc. 125 (1997), 259-268 Request permission

Abstract:

It is shown that

[(1)] a locally compact convex subset $C$ of a topological vector space that admits a sequence of continuous affine functionals separating points of $C$ affinely embeds into a Hilbert space;

[(2)] an infinite-dimensional locally compact convex subset of a metric linear space has a central point;

[(3)] every $\sigma$-compact locally convex metric linear space topologically embeds onto a pre-Hilbert space.

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