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Coincidence Sets of Coincidence Producing Maps

Published online by Cambridge University Press:  20 November 2018

Helga Schirmer
Helga Schirmer*
Affiliation:
Carleton UniversityOttawa, Canada
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Abstract

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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.

Keywords

Primary 55M20Secondary 54H25Coincidencesrealization of coincidence setscoincidence producing mapsuniversal mapsunit ball
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 26 , Issue 2 , 01 June 1983 , pp. 167 - 170
Copyright
Copyright © Canadian Mathematical Society 1983

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