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An Embedding Theorem for Separable Locally Convex Spaces

Published online by Cambridge University Press:  20 November 2018

Robert H. Lohman
Robert H. Lohman*
Affiliation:
Kent State University, Kent, Ohio
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A well-known embedding theorem of Banach and Mazur [1, p. 185] states that every separable Banach space is isometrically isomorphic to a subspace of C[0, 1], establishing C[0, 1] as a universal separable Banach space. The embedding theorem one encounters in a course in topological vector spaces states that every Hausdorff locally convex space (l.c.s.) is topologically isomorphic to a subspace of a product of Banach spaces.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 119 - 120
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Banach, S., Théorie des opérations linéaires, Warsaw, 1932.Google Scholar
2. Kelley, J. L. and Namioka, I., Linear topological spaces, Princeton Univ. Press, Princeton, N.J., 1963.Google Scholar
3. Pondiczery, E. S., Power problems in abstract spaces, Duke Math. J. 11 (1944), 835-837.Google Scholar