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

 

On separability in linear topological spaces


Authors: Robert H. Lohman and Wilbur J. Stiles
Journal: Proc. Amer. Math. Soc. 42 (1974), 236-237
MSC: Primary 46A99
MathSciNet review: 0326350
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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 [Enhancements On Off] (What's this?)

  • [1] Haskell P. Rosenthal, On quasi-complemented subspaces of Banach spaces, with an appendix on compactness of operators from 𝐿^{𝑝}(𝜇) to 𝐿^{𝑟}(𝜈), J. Functional Analysis 4 (1969), 176–214. MR 0250036 (40 #3277)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1974-0326350-X
PII: S 0002-9939(1974)0326350-X
Keywords: Separable linear space, nonseparable linear subspace, metrizable linear subspace
Article copyright: © Copyright 1974 American Mathematical Society