Geodesic
Coincidence Sets of Coincidence Producing Maps
Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 167-170

Voir la notice de l'article provenant de la source Cambridge University Press

A theorem by H. Robbins shows that every closed and non-empty subset of the unit ball Bn in Euclidean n-space is the fixed point set of a self map of Bn. This result is extended to coincidence producing maps of Bn, where a map ƒ:X → Y is coincidence producing (or universal) if it has a coincidence with every map g:X → Y. The main result implies that if ƒ:Bn, Sn - 1 → Bn, Sn - 1 is coincidence producing and A⊂Bn closed and nonempty, then there exist a map ƒ': Bn, Sn - 1 → Bn, Sn - 1 and a map g: Bn → Bn such that ƒ' | Sn - 1 is homotopic to ƒ | Sn-1 and A is the coincidence set of ƒ' and g.
DOI : 10.4153/CMB-1983-027-6
Mots-clés : Primary 55M20, Secondary 54H25, Coincidences, realization of coincidence sets, coincidence producing maps, universal maps, unit ball 
Schirmer, Helga. Coincidence Sets of Coincidence Producing Maps. Canadian mathematical bulletin, Tome 26 (1983) no. 2, pp. 167-170. doi: 10.4153/CMB-1983-027-6
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