Abstract
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 \((E,T(\mathcal{U}),T((\mathcal{U}^{ - 1} ))\) is a pairwise Baire bitopological space, where \(\mathcal{U}\), is a quasi-uniformity that determines, in L. Nachbin's sense, the topological ordered space E.
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Alegre, C., Ferrer, J. & Gregori, V. On a class of real normed lattices. Czechoslovak Mathematical Journal 48, 785–792 (1998). https://doi.org/10.1023/A:1022499925483
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DOI: https://doi.org/10.1023/A:1022499925483