2012-11 Dividing a circle

Let f be a continuous function from [0,1] such that f([0,1]) is a circle. Prove that there exists two closed intervals \(I_1, I_2 \subseteq [0,1]\) such that \(I_1\cap I_2\) has at most one point, \(f(I_1)\) and \(f(I_2)\) are semicircles, and \(f(I_1)\cup f(I_2)\) is a circle.

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4 thoughts on “2012-11 Dividing a circle

  1. hunminpark

    문제에서 마지막의 circle과 함수 f의 공역 circle이 동일한 circle인가요?

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