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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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 $C$ 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

Czeslaw 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
Email: tdobrowo@mail.pittstate.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03832-X
PII: S 0002-9939(97)03832-X
Keywords: Convex set, affine embedding, locally convex space, central points, $\sigma $-compact spaces
Received by editor(s): July 21, 1992
Communicated by: James E. West
Article copyright: © Copyright 1997 American Mathematical Society