On separability in linear topological spaces

Lohman, Robert H.; Stiles, Wilbur J.

doi:10.1090/S0002-9939-1974-0326350-X

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On separability in linear topological spaces
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by Robert H. Lohman and Wilbur J. Stiles PDF

Proc. Amer. Math. Soc. 42 (1974), 236-237 Request permission

Abstract:

This paper contains (1) an example of a separable linear topological space with a closed nonseparable linear subspace, and (2) a proof of the fact that every metrizable subspace of a separable linear topological space is separable.

References

Haskell P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from $L^{p}\,(\mu )$ to $L^{r}\,(\nu )$, J. Functional Analysis 4 (1969), 176–214. MR 0250036, DOI 10.1016/0022-1236(69)90011-1