# 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 51 subcategories, out of 51 total.

### B

### C

### D

### E

### G

### H

### I

### M

### N

### O

### P

### R

### S

### T

## Pages in category "Mapping Theory"

The following 93 pages are in this category, out of 93 total.

### C

- Cantor's Diagonal Argument
- 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

- Element in Image of Preimage under Mapping
- Embedding Ring into Ring Structure Induced by Ring Operations
- Empty Mapping is Mapping
- Empty Mapping is Unique
- Equality of Elements in Range of Mapping
- Equality of Mappings
- Equality of Mappings/Also defined as
- Equivalence of Definitions of Image of Mapping
- Equivalence of Definitions of Mapping

### 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
- 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 of Union under Mapping/Family of Sets
- Image of Union under Mapping/General Result
- Image Preserves Subsets
- Induced Structure Identity
- Induced Structure Inverse
- Inductive Definition of Sequence
- Intersection of Image with Subset of Codomain
- Isomorphism to Closed Interval

### M

### P

### R

### S

- Second Principle of Recursive Definition
- Set of all Self-Maps is Monoid
- Set of All Self-Maps is Semigroup
- Set of Mappings which map to Same Element induces Equivalence Relation
- Strictly Monotone Mapping is Monotone
- Structure Induced by Abelian Group Operation is Abelian Group
- Structure Induced by Associative Operation is Associative
- Structure Induced by Commutative Operation is Commutative
- Structure Induced by Commutative Ring Operations is Commutative Ring
- Structure Induced by Group Operation is Group
- Structure Induced by Ring Operations is Ring
- Structure Induced by Ring with Unity Operations is Ring with Unity
- Subset Maps to Subset
- Subset of Set with Propositional Function
- Sum of Positive and Negative Parts

### U

- Union of Bijections with Disjoint Domains and Codomains is Bijection
- Union of Functions Theorem
- Union of Mappings which Agree is Mapping
- Union of Mappings with Disjoint Domains is Mapping
- Unit of Ring of Mappings iff Image is Subset of Ring Units
- Unit of Ring of Mappings iff Image is Subset of Ring Units/Image is Subset of Ring Units implies Unit of Ring of Mappings
- Unit of Ring of Mappings iff Image is Subset of Ring Units/Unit of Ring of Mappings implies Image is Subset of Ring Units