Hostname: page-component-76fb5796d-vfjqv Total loading time: 0 Render date: 2024-04-28T05:25:35.349Z Has data issue: false hasContentIssue false

A Brouwer Type Coincidence Theorem and the Fundamental Theorem of Algebra

Published online by Cambridge University Press:  20 November 2018

M. M. Dodson*
Affiliation:
Department of Mathematics, University of York, Heslington, York, Y01 5DD, Great Britain
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that a coincidence theorem which is a natural generalisation of Brouwer's fixed point theorem also gives a short and simple proof of the fundamental theorem of algebra.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1984

References

1. Brown, R. F., Coincidences Of Maps Of Euclidean Spaces. Amer. Math. Monthly 75 (1968), 523-525.Google Scholar
2. Bryszewski, J. and Gorniewicz, L., A Poincare type coincidence theorem for multi-valued maps. Bull. Acad. Polon. Sci. Ser. sci., math., astr. et phys. 24 (1976), 593-598.Google Scholar
3. Eilenberg, S. and Niven, I., The “Fundamental Theorem of Algebra” for quaternions. Bull. Amer. Math. Soc. 50 (1944), 246-248.CrossRefGoogle Scholar
4. Komarov, I. Yu., On points of coincidence for two transformations (in Russian). Vest. Mosk. Univ. 2 (1976), 11-14.Google Scholar
5. Reich, S., A Poincare type concidence theorem. Amer. Math. Monthly 81 (1974), 52-53.Google Scholar
6. Schirmer, H., A Brouwer type coincidence theorem. Canad. Math. Bull. 9 (1966), 443-446.10.4153/CMB-1966-053-3CrossRefGoogle Scholar
7. Schirmer, H., A Kakutani type coincidence theorem. Fund. Math. 69 (1970), 219-226.CrossRefGoogle Scholar
8. Spanier, E. H., Algebraic Topology. Springer-Verlag, New York 1966.Google Scholar