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Let X and Y be non-empty sets and f a mapping of X into Y. Show that f is onto iff there exists a mapping h of Y into X such that fh = iX.

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Topology
Sets and Functions (XXXVIII)
Functions

Let X and Y be non-empty sets and f a mapping of X into Y.
Show that f is onto iff there exists a mapping h of Y into X such that fh = iX.

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Topology
Sets and Functions (XXXVIII)
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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 onto iff there exists a mapping h of Y into X such that fh = iX.

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