# Category:Mapping Theory

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This category contains results about Mapping Theory.

Definitions specific to this category can be found in Definitions/Mapping Theory.

**Mapping theory** is the subfield of set theory concerned with the properties of mappings.

## Subcategories

This category has the following 68 subcategories, out of 68 total.

### B

### C

- Closedness under Mappings (1 P)
- Complex Functions (empty)

### D

- Decreasing Mappings (3 P)

### E

- Empty Mapping (6 P)
- Examples of Multifunctions (empty)
- Examples of Preimages of Mappings (empty)
- Examples of Solution Sets (4 P)

### F

### G

- Graphs of Mappings (4 P)

### H

### I

- Idempotent Mappings (2 P)
- Image of Subset under Mapping (empty)
- Image of Union under Mapping (5 P)
- Inclusion Mappings (24 P)
- Involutions (9 P)

### L

### M

- Many-to-One Relations (1 P)
- Monotone Mappings (4 P)

### N

### O

### P

- Parametric Equations (empty)

### Q

- Quotient Theorem for Sets (4 P)

### R

### S

- Successor Mapping (2 P)
- Symmetric Functions (empty)

### T

- Translation Mappings (8 P)

### U

- Union Mappings (4 P)

### W

- Well-Defined Mappings (4 P)

## Pages in category "Mapping Theory"

The following 69 pages are in this category, out of 69 total.

### C

- Cantor's Diagonal Argument
- Cardinality of Extensions of Function on Subset of Finite Set
- Cardinality of Image of Mapping not greater than Cardinality of Domain
- Cardinality of Image of Set not greater than Cardinality of Set
- Cardinality of Mapping
- Cardinality of Set of All Mappings
- Cardinality of Set of All Mappings from Empty Set
- Cardinality of Set of All Mappings to Empty Set
- Complement of Preimage equals Preimage of Complement
- Composition of Commuting Idempotent Mappings is Idempotent
- Composition of Inflationary and Idempotent Mappings
- Condition for Agreement of Family of Mappings

### D

### E

### F

### I

- Image is Subset of Codomain/Corollary 2
- Image is Subset of Codomain/Corollary 3
- Image of Countable Set under Mapping is Countable
- Image of Domain of Mapping is Image Set
- Image of Empty Set is Empty Set/Corollary 1
- Image of Intersection under Mapping
- Image of Intersection under Mapping/Family of Sets
- Image of Intersection under Mapping/General Result
- Image of Inverse Image
- Image of Mapping from Finite Set is Finite
- Image of Pair under Mapping
- Image of Set Difference under Mapping
- Image of Singleton under Mapping
- Image of Subset under Mapping equals Union of Images of Elements
- Image of Subset under Mapping is Subset of Image
- Image of Subset under Relation is Subset of Image/Corollary 1
- Image of Union under Mapping
- Image Preserves Subsets
- Inductive Definition of Sequence
- Intersection of Image with Subset of Codomain
- Isomorphism to Closed Interval