Скачать или смотреть Brouwer Fixed Point Theorem in Dimension One! (FAMOUS Calculus Proof in Algebraic Topology)

The Brouwer Fixed Point Theorem is a famous result in algebraic topology in all dimensions, but the one-dimensional version is a calculus theorem that can be understood by calculus students. In this video, I explain the proof of the one-dimensional version rigorously as well as explain how to think about rigorous math and write math proofs. The proof is based on a version of the intermediate value theorem in calculus. In the end of the video, I will explain the general statement (that can only be proved with the advanced graduate level machinery of algebraic topology) in an accessible manner. 🥳

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