Abstract
In order to have a topological category that contains both pMET and Unif in a nice way (and therefore combines quantitative and uniform concepts), approach uniformities are introduced. Approach uniformities uniformize the so-called approach spaces, introduced in Lowen [8]. Different characterizations of approach uniformities are formulated. Some natural examples are presented, such as function spaces, hyperspaces, spaces of measures, and an example concerning theoretical computer science.