TOUCHE ROUCHE

Abstract

There seems to be a love-hate relationship between Brouwer's fixed point theorem and the fundamental theorem of algebra; in this note we offer one more tweak at it, and give a version of Rouches theorem.

Keywords

• contractible mapping;
• Brouwer fixed point theorem;
• fundamental theorem of algebra;
• Rouche′s theorem

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References

1. Amer. Math. Monthly v.56 A topological proof of the fundamental theorem of algebra B.H.Arnold https://doi.org/10.2307/2305130
2. Topology and analysis: the Atiyah-Singer formula and gauge-theoretic physics B.Booss;D.D.Bleecker
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4. Functions of one complex variable J.B.Conway
5. Invertibility and singularity R.E.Harte
6. An introduction to algebraic topology J.J.Rotman
7. Notices Amer. Math. Soc. v.104 Borsuk-Ulam implies Brouwer, a direct construction F.E.Su
8. Amer. Math. Monthly v.96 A version of Rouches theorem for continuous functions A.Tsarpalias https://doi.org/10.2307/2324586

Cited by

1. Ruston, Riesz and perturbation classes vol.389, pp.2, 2012, https://doi.org/10.1016/j.jmaa.2011.12.030