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On a class of real normed lattices

C. Alegre; Jesús Ferrer; Valentín Gregori — 1998

Czechoslovak Mathematical Journal

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 $(E, T (𝒰), T (𝒰^{- 1}))$ , is a pairwise Baire bitopological space, where $𝒰$ , is a quasi-uniformity that determines, in $L$ . Nachbin’s sense, the topological ordered space $E$ .

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