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Proposition: FixedPoint Property of Continuous Functions on Closed Intervals
Let $[a,b]$ be a closed real interval and let $f:[a,b]\to[a,b]$ be a continuous function. Then $f$ has a fixed point property, i.e. there is an $x\in[a,b]$ with $f(x)=x.$
Table of Contents
Proofs: 1
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References
Bibliography
 Forster Otto: "Analysis 1, Differential und Integralrechnung einer VerĂ¤nderlichen", Vieweg Studium, 1983