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

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