## Two characterizations of linear Baire spaces

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- by Stephen A. Saxon PDF
- Proc. Amer. Math. Soc.
**45**(1974), 204-208 Request permission

## Abstract:

The Wilansky-Klee conjecture is equivalent to the (unproved) conjecture that every dense, $1$-codimensional subspace of an arbitrary Banach space is a Baire space (second category in itself). The following two characterizations may be useful in dealing with this conjecture: (i) A topological vector space is a Baire space if and only if every absorbing, balanced, closed set is a neighborhood of some point, (ii) A topological vector space is a Baire space if and only if it cannot be covered by countably many nowhere dense sets, each of which is a union of lines ($1$-dimensional subspaces). Characterization (i) has a more succinct form, using the definition of Wilansky’s text [8, p. 224]: a topological vector space is a Baire space if and only if it has the $t$ property.## References

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*(LF)-spaces, quasi-Baire spaces, and the strongest locally convex topology*(to appear).

## Additional Information

- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**45**(1974), 204-208 - MSC: Primary 46A15
- DOI: https://doi.org/10.1090/S0002-9939-1974-0358274-6
- MathSciNet review: 0358274