We present an axiomatic theory, based on the notions of metric space and space with a (first order) neighbour relation. The axiomatics implies a synthetic proof of Huygens' principle of wave fronts, as envelopes of a family of spheres. A model of the axiomatics is presented in terms of synthetic differential geometry (SDG).
Keywords: metric spaces, synthetic differential geometry
2010 MSC: 51K10, 18B40, 18D99, 51Fxx
Theory and Applications of Categories, Vol. 32, 2017, No. 24, pp 803-822.
Revised 2017-07-31. Original version at