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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.

https://brainmass.com/math/geometry-and-topology/142539

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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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