Maps on D₁ and D₂ spaces

Abstract

A space X is said to be Z), provided each closed set has a countable basis for the open sets containing it. It is said to be D 2 provided there is a countable base {(/"} such that each closed set has a countable base for the open sets containing it, which is a subfamily of {£/"}. In this paper, we give a separation theorem for D x spaces, and provide a characterization of D, and D 2 spaces in terms of maps.