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/