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Zbl 0949.54045
Alegre, C.; Ferrer, J.; Gregori, V.
On a class of real normed lattices.
(English)
[J] Czech. Math. J. 48, No.4, 785-792 (1998). ISSN 0011-4642; ISSN 1572-9141/e

Summary: We say that a real normed lattice is quasi-Baire if the intersection of each sequence of monotonic open dense sets is dense. An example of a Baire-convex space, due to M. Valdivia, which is not quasi-Baire is given. We obtain that $E$ is a quasi-Baire space iff $(E, T({\cal U}),T({\cal U}^{-1}))$ is a pairwise Baire bitopological space, where ${\cal U}$ is a quasi-uniformity that determines, in Nachbin's sense, the topological ordered space $E$.
MSC 2000:
*54F05 Ordered topological spaces
54E52 Baire category, Baire spaces
54E55 Bitopologies
54E15 Uniform structures and generalizations

Keywords: barrelled space; convex-Baire space; normed lattice; pairwise Baire spaces; quasi-Baire spaces; quasi-uniformity

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