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    Consider an arbitrary mapping f : X -->Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: f^(-1)(Y) = X

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    Topology
    Sets and Functions (XXVIII)
    Functions

    Consider an arbitrary mapping f : X -->Y. Suppose that f is a one-to-one onto.
    Prove the main property of the second set mapping:

    f^(-1)(Y) = X

    See the attached file.

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    Topology
    Sets and Functions (XXVIII)
    ...

    Solution Summary

    This solution is comprised of a detailed explanation of the main property of the second set mapping.
    It contains step-by-step explanation of the following problem:
    Consider an arbitrary mapping f : X -->Y. Suppose that f is a one-to-one onto.
    Prove the main property of the second set mapping:

    f^(-1)(Y) = X

    Notes are also given at end.

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