Metrizability of certain point-countable unions. (English) Zbl 1032.54017

Tanaka, Yoshio

Sci. Math. Jpn. 57, No. 2, 201-206 (2003).

The author considers modifications of certain metrizability theorems for spaces having a point-countable cover by metrizable subspaces which determines the topology of the space. The modifications are obtained by replacing the assumption that the point-countable cover determines the topology with a weaker assumption that the topology is determined by the collection of all the finite unions of the elements of this cover.

Reviewer: Jozef Chaber (Warszawa)

MSC:

54E35	Metric spaces, metrizability
54B15	Quotient spaces, decompositions in general topology
54D55	Sequential spaces

Keywords:

metrizability; weak topology; sequential space; sequential fan; Arens’ space