inverse image
Let be a function, and let be a subset. The inverse image of is the set consisting of all elements such that .
The inverse image commutes with all set operations: For any collection of subsets of , we have the following identities for
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1.
Unions:
- 2.
and for any subsets and of , we have identities for
- 3.
- 4.
- 5.
In addition, for and , the inverse image satisfies the miscellaneous identities
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6.
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7.
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8.
, with equality if is injective.
Title | inverse image |
Canonical name | InverseImage |
Date of creation | 2013-03-22 11:51:58 |
Last modified on | 2013-03-22 11:51:58 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 10 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 03E20 |
Classification | msc 46L05 |
Classification | msc 82-00 |
Classification | msc 83-00 |
Classification | msc 81-00 |
Synonym | preimage |
Related topic | Mapping |
Related topic | DirectImage |