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.