Characterization of bases of countable order and factorization of monotone developability. (English) Zbl 0967.54027

Hung, H. H.

Topol. Proc. 23(Summer), 207-220 (1998).

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.

Reviewer: H.Brandenburg (Berlin)

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

Keywords:

base of countable order; monotonically developable space