Geodesic
A Brouwer Type Coincidence Theorem
Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 443-446

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Brouwer's celebrated fixed point theorem states that every map of a closed n-cell into itself has a fixed point.A similar theorem is here proved for coincidences between a pair of maps (f, g): In→In, where I denotes a closed n-cell (i.e. a homeomorph of the n-ball) and a coincidence is a point x∊In for which f(x)=g(x). That two arbitrary maps (f, g): In→In need not have a coincidence is shown by the pair f:In→y0, g:In→y1, where y0, y1∊In and y0≠y1. More generally, one can immediately construct a map g so that (f, g) is coincidence free if f is not surjective. 
Schirmer, Helga. A Brouwer Type Coincidence Theorem. Canadian mathematical bulletin, Tome 9 (1966) no. 4, pp. 443-446. doi: 10.4153/CMB-1966-053-3
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     author = {Schirmer, Helga},
     title = {A {Brouwer} {Type} {Coincidence} {Theorem}},
     journal = {Canadian mathematical bulletin},
     pages = {443--446},
     year = {1966},
     volume = {9},
     number = {4},
     doi = {10.4153/CMB-1966-053-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-053-3/}
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