Geodesic
Ordered spaces with special bases
Fundamenta Mathematicae, Tome 158 (1998) no. 3, pp. 289-299.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

We study the roles played by four special types of bases (weakly uniform bases, ω-in-ω bases, open-in-finite bases, and sharp bases) in the classes of linearly ordered and generalized ordered spaces. For example, we show that a generalized ordered space has a weakly uniform base if and only if it is quasi-developable and has a $G_δ$-diagonal, that a linearly ordered space has a point-countable base if and only if it is first-countable and has an ω-in-ω base, and that metrizability in a generalized ordered space is equivalent to the existence of an OIF base and to the existence of a sharp base. We give examples showing that these are the best possible results.
DOI : 10.4064/fm-158-3-289-299
Keywords: point-countable base, weakly uniform base, ω-in-ω base, open-in-finite base, sharp base, metrizable space, quasi-developable space, linearly ordered space, generalized ordered space

Harold Bennett 1 ; David Lutzer 1

1 
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Harold Bennett; David Lutzer. Ordered spaces with special bases. Fundamenta Mathematicae, Tome 158 (1998) no. 3, pp. 289-299. doi : 10.4064/fm-158-3-289-299. http://geodesic.mathdoc.fr/articles/10.4064/fm-158-3-289-299/

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