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# Topology and mapping functions

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Topology
Sets and Functions (XXXIV)
Functions

Let X be a non-empty set. The identity mapping ix on X is the mapping of X onto itself
defined by ix(x) = x for every x. Thus ix sends each element of X to itself; that is,
it leaves fixed each element of X. Show that f ix = ix f = f for any mapping f of X into
itself.

See the attached file.

##### Solution Summary

This solution is comprised of a detailed explanation that f ix = ix f = f for any mapping f of X into itself.
It contains step-by-step explanation of the following problem:

Let X be a non-empty set. The identity mapping ix on X is the mapping of X onto itself
defined by ix(x) = x for every x. Thus ix sends each element of X to itself; that is,
it leaves fixed each element of X. Show that f ix = ix f = f for any mapping f of X into
itself.

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###### Education
• BSc, Manipur University
• MSc, Kanpur University
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