A note on nets and metrization

Abstract

A collection _ of subsets of a topological space X is ane$ for X if for each point x in X and open neighborhood U of x there exists a B e .s uch that x e B U. A space with a a-locally finite net is called a a-space and a regular space with a countable net is called a cosmic space (A. Okuyama [15] and E. Michael [7]). We assume at least T for every topological space throughout this paper. For terminol- ogy not defined here, see J. Nagata [11].