With Davorin LeÅ¡nik.

**Abstract:** We investigate the relationship between constructive theory of metric spaces and synthetic topology. Connections between these are established by requiring a relationship to exist between the intrinsic and the metric topology of a space. We propose a non-classical axiom which has several desirable consequences, e.g., that all maps between separable metric spaces are continuous in the sense of metrics, and that, up to topological equivalence, a set can be equipped with at most one metric which makes it complete and separable.

**Presented at:** *3rd Workshop on Formal Topology*

**Download slides:** 3wft.pdf