Fragmentability by the Discrete Metric

Abstract

In a recent paper, topological spaces (X, τ) that are fragmented by a metric that generates the discrete topology were investigated. In the present paper we shall continue this investigation. In particular, we will show, among other things, that such spaces are σ-scattered, that is, a countable union of scattered spaces, and characterise the continuous images of separable metrisable spaces by their fragmentability properties.2010 Mathematics subject classification: primary 46B20; secondary 46B22.