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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:
 5.4e+36 Metric spaces, metrizability 5.4e+31 Moore spaces 5.4e+21 Stratifiable spaces, cosmic spaces, etc. 5.4e+19 $$p$$-spaces, $$M$$-spaces, $$\sigma$$-spaces, etc. 5.4e+100 Topological spaces with richer structures 5.4e+26 Semimetric spaces
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