Geodesic
Metric spaces and SDG
Theory and applications of categories, Tome 32 (2017), pp. 803-822.

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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).
Publié le :
Classification : 51K10, 18B40, 18D99, 51Fxx
Keywords: metric spaces, synthetic differential geometry 
@article{TAC_2017_32_a23,
     author = {Anders Kock},
     title = {Metric spaces and {SDG}},
     journal = {Theory and applications of categories},
     pages = {803--822},
     publisher = {mathdoc},
     volume = {32},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2017_32_a23/}
}
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Anders Kock. Metric spaces and SDG. Theory and applications of categories, Tome 32 (2017), pp. 803-822. http://geodesic.mathdoc.fr/item/TAC_2017_32_a23/