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    Homotopy equivalence and homotopy are equivalence relations

    P-UNL871F13-HAT0-03

    Area
    Topology
    Topics
    Homotopy
    Status
    draft
    Contents

    1. Show that the composition of homotopy equivalences \(X\to Y\) and \(Y\to Z\) is a homotopy equivalence \(X\to Z\). Deduce that homotopy equivalence is an equivalence relation.

    2. Show that homotopy among maps \(X\to Y\) is an equivalence relation.

    3. Show that a map homotopic to a homotopy equivalence is itself a homotopy equivalence.

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