ON THE STRUCTURE OF THE SPACE OF METRICS DEFINED ON A GIVEN SET

Abstract

This paper is a continuation of the authors’ earlier paper [4]. Denote by $\mathcal{M}$ the metric space of all metrics on a given nonvoid set $X$ with the sup-metric. In this paper some subsets of $\mathcal{M}$ are investigated, namely subsets consisting of all metrics $d\in \mathcal{M}$ for which $(X,d)$ possesses prescribed topological (metric) properties.