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 -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.
@article{bwmeta1.element.bwnjournal-article-fmv158i3p289bwm,
author = {Harold Bennett and David Lutzer},
title = {Ordered spaces with special bases},
journal = {Fundamenta Mathematicae},
volume = {158},
year = {1998},
pages = {289-299},
zbl = {0936.54030},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv158i3p289bwm}
}
Bennett, Harold; Lutzer, David. Ordered spaces with special bases. Fundamenta Mathematicae, Tome 158 (1998) pp. 289-299. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv158i3p289bwm/
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