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    Let X and Y be non-empty sets and f a mapping of X into Y. Show that f is one-to-one iff there exists a mapping g of Y into X such that gf = iX.

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    Topology
    Sets and Functions (XXXVII)
    Functions

    Let X and Y be non-empty sets and f a mapping of X into Y.
    Show that f is one-to-one iff there exists a mapping g of Y into X such that gf = iX.

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    Topology
    Sets and Functions (XXXVII)
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    Solution Summary

    This solution is comprised of a detailed explanation of the properties of the mappings.
    It contains step-by-step explanation of the following problem:

    Let X and Y be non-empty sets and f a mapping of X into Y.
    Show that f is one-to-one iff there exists a mapping g of Y into X such that gf = iX.

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