A note on nets and metrization
Francis Siwiec, Jun-iti Nagata · Proceedings of the Japan Academy Series A Mathematical Sciences · 1968
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 .such 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].A collection of closed subsets of a topological space X is a c-ne for X if for any different points x, such that x e F and x'e F. A space with a a-closure preserving cnet is called a a-space.A base _ for a space X is poin countable if each point x of X is in at most countably many members of . .