# On a class of real normed lattices

C. Alegre; Jesús Ferrer; Valentín Gregori

Czechoslovak Mathematical Journal (1998)

- Volume: 48, Issue: 4, page 785-792
- ISSN: 0011-4642

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topAlegre, C., Ferrer, Jesús, and Gregori, Valentín. "On a class of real normed lattices." Czechoslovak Mathematical Journal 48.4 (1998): 785-792. <http://eudml.org/doc/30454>.

@article{Alegre1998,

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 $E$.},

author = {Alegre, C., Ferrer, Jesús, Gregori, Valentín},

journal = {Czechoslovak Mathematical Journal},

keywords = {Barrelled space; convex-Baire space; normed lattice; pairwise Baire spaces; quasi-Baire spaces; quasi-uniformity; barrelled space; convex-Baire space; normed lattice; pairwise Baire spaces; quasi-Baire spaces; quasi-uniformity},

language = {eng},

number = {4},

pages = {785-792},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On a class of real normed lattices},

url = {http://eudml.org/doc/30454},

volume = {48},

year = {1998},

}

TY - JOUR

AU - Alegre, C.

AU - Ferrer, Jesús

AU - Gregori, Valentín

TI - On a class of real normed lattices

JO - Czechoslovak Mathematical Journal

PY - 1998

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 48

IS - 4

SP - 785

EP - 792

AB - 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 $E$.

LA - eng

KW - Barrelled space; convex-Baire space; normed lattice; pairwise Baire spaces; quasi-Baire spaces; quasi-uniformity; barrelled space; convex-Baire space; normed lattice; pairwise Baire spaces; quasi-Baire spaces; quasi-uniformity

UR - http://eudml.org/doc/30454

ER -

## References

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- Quasi-uniform Spaces, Marcel Dekker Inc. New York, 1982. (1982) MR0660063
- Bitopological spaces, Proc. London Math. Soc. (3) 13 (1963), 71–89. (1963) Zbl0107.16401MR0143169
- Topology and Order, Robert E. Kriegler Publishing Co., Huntington, New York, 1976. (1976) Zbl0333.54002MR0415582
- Topics in Locally Convex Spaces, North-Holland, Amsterdam, 1982. (1982) Zbl0489.46001MR0671092

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