# 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.

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.

See the attached file.

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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.