Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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TOUCHE ROUCHE

  • Harte, Robin (School of Mathematics, Trinity College) ;
  • Keogh, Gary (Computer Applications, Dublin City University)
  • Published : 2003.05.01

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

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