direct image
Let be a function, and let be a subset. The direct image of is the set consisting of all elements of which equal for some .
Direct images satisfy the following properties:
- 1.
Unions: For any collection
of subsets of ,
- 2.
Intersections
: For any collection of subsets of ,
- 3.
Set difference
: For any ,
In particular, the complement of satisfies .
- 4.
Subsets: If , then .
- 5.
Inverse image
of a direct image: For any ,
with equality if is injective
.
- 6.
Direct image of an inverse image: For any ,
with equality if is surjective
.
Title | direct image |
Canonical name | DirectImage |
Date of creation | 2013-03-22 11:52:01 |
Last modified on | 2013-03-22 11:52:01 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 10 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 03E20 |
Classification | msc 81-00 |
Classification | msc 18-00 |
Classification | msc 17B37 |
Classification | msc 18D10 |
Classification | msc 18D35 |
Classification | msc 16W30 |
Synonym | image |
Related topic | InverseImage |
Related topic | Mapping |