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Characterization of bases of countable order and factorization of monotone developability. (English) Zbl 0967.54027
Spaces with a base of countable order (also called monotonically developable spaces) are a natural generalization of developable spaces. They have been characterized, for example, by J. M. Worrell jun. and H. H. Wicke [Can. J. Math. 17, 820-830 (1965; Zbl 0132.18401)] and by J. Chaber, M. M. Čoban and K. Nagami [Fundam. Math. 84, 107-119 (1974; Zbl 0292.54038)]. This paper contains three new characterizations in terms which are too technical to be cited here. It is pointed out that the earlier characterizations can be deduced from these results.

MSC:
54E35 Metric spaces, metrizability
54E30 Moore spaces
54E20 Stratifiable spaces, cosmic spaces, etc.
54E18 \(p\)-spaces, \(M\)-spaces, \(\sigma\)-spaces, etc.
54E99 Topological spaces with richer structures
54E25 Semimetric spaces
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