Fragmentability and scatteredness in topological spaces

Abstract

In this paper we deal with the fragmentability of the topological space (X, τ 1) by a metric which generates the topology τ 2 on X where τ 2 is not necessarily distinct from τ 1. Also we investigate the relation between ω-scatteredness and fragmentability by a metric that generates the discrete topology. In particular we will show that in locally hereditarily Lindelof spaces, fragmentability by a metric that generates the discrete topology and ω-scatteredness are equivalent.