Two characterizations of linear Baire spaces
Author:
Stephen A. Saxon
Journal:
Proc. Amer. Math. Soc. 45 (1974), 204208
MSC:
Primary 46A15
MathSciNet review:
0358274
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Abstract: The WilanskyKlee conjecture is equivalent to the (unproved) conjecture that every dense, 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 (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 property.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197403582746
PII:
S 00029939(1974)03582746
Keywords:
WilanskyKlee conjecture,
topological vector spaces,
Baire spaces,
absorbing,
balanced,
closed set,
unordered Bairelike spaces
Article copyright:
© Copyright 1974
American Mathematical Society
