Search the corpus

    Quotient a set by the fibers of a surjection

    P-UNL871F13-MUN3.4

    Area
    Topology
    Topics
    Equivalence Relations
    Status
    draft
    Contents

    Let \(f:A\to B\) be a surjective function. Define a relation on \(A\) by \[ a_0\sim a_1\quad\Longleftrightarrow\quad f(a_0)=f(a_1). \]

    1. Show that \(\sim\) is an equivalence relation.

    2. Let \(A^*\) be the set of equivalence classes. Show that there is a bijective correspondence between \(A^*\) and \(B\).

    Solution submission

    Submit a solution on GitHub

    Source Collections