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On a class of real normed lattices (1998)

Alegre, C. ; Ferrer, J. ; Gregori, V.

Springer

Czechoslovak mathematical journal 48 (1998), S. 785-792

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ISSN: 1572-9141

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

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: 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.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1022499925483

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