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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Additional Information
- Czesław Bessaga
- Affiliation: Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
- Email: bessaga@impan.impan.gov.pl
- Tadeusz Dobrowolski
- Affiliation: Instytut Matematyki, Uniwersytet Warszawski, ul. Banacha 2, 02-097 Warszawa, Poland
- Address at time of publication: Department of Mathematics, Pittsburg State University, Pittsburg, Kansas 66762
- MR Author ID: 58620
- Email: tdobrowo@mail.pittstate.edu
- Received by editor(s): July 21, 1992
- Communicated by: James E. West
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 259-268
- MSC (1991): Primary 57N17
- DOI: https://doi.org/10.1090/S0002-9939-97-03832-X
- MathSciNet review: 1389505