### Abstract

A first order structure M equipped with a dense linear ordering is called weakly o-minimal iff all definable subsets of M are finite unions of convex sets. In the first part of the talk we will discuss some properties of the topological dimension of sets definable in weakly o-minimal structures. This will constitute a basis for the second part which will be focused on the problem of topologisation of groups, group actions and fields definable in weakly o-minimal structures.