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A simple proof of P. Carter’s theorem
1997
We give a simple proof of the following result of P. Carter: Given a twist homeomorphism of an annulus with at most one fixed point in the interior of the annulus, then there exists an essential simple closed curve inside this annulus meeting its image in at most the (possible) interior fixed point.
Keywords:
- Bruck–Ryser–Chowla theorem
- Fixed-point theorem
- Fixed point
- Kakutani fixed-point theorem
- Brouwer fixed-point theorem
- Poincaré–Birkhoff theorem
- Kelvin–Stokes theorem
- Proofs of Fermat's little theorem
- Mathematical analysis
- Mathematics
- Mean value theorem
- Discrete mathematics
- Jordan curve theorem
- Pure mathematics
- Picard–Lindelöf theorem
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