# 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

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.

© BrainMass Inc. brainmass.com October 9, 2019, 8:11 pm ad1c9bdddfhttps://brainmass.com/math/geometry-and-topology/142539

#### Solution Preview

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.