Affine and homeomorphic embeddings into ℓ²

Bessaga, Czesław; Dobrowolski, Tadeusz

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

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Affine and homeomorphic embeddings into $\ell ^{2}$

Authors: Czeslaw Bessaga and Tadeusz Dobrowolski
Journal: Proc. Amer. Math. Soc. 125 (1997), 259-268
MSC (1991): Primary 57N17
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Abstract: It is shown that

(1): a locally compact convex subset of a topological vector space that admits a sequence of continuous affine functionals separating points of 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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