Category:Mapping Theory

B

• [+] Bijections‎ (1 C, 38 P)

C

• [×] Characteristic Functions‎ (9 P)
• [×] Composite Mappings‎ (9 P)
• [+] Continuity‎ (3 C, 43 P)

H

• [+] Homomorphisms‎ (10 C, 25 P)

I

• [×] Induced Mappings‎ (4 P)
• [×] Injections‎ (41 P)
• [×] Inverse Mappings‎ (29 P)

R

• [+] Relation Theory‎ (11 C, 45 P)

S

• [×] Sequences‎ (15 P)
• [×] Surjections‎ (43 P)

C

• Cantor's Diagonal Argument
• Cardinality of Set of All Mappings
• Constant Mapping both Increasing and Decreasing
• Constant Mapping has Singleton Image

D

• Difference of Positive and Negative Parts
• Dominates is Equivalent to Subset

E

• Equality of Elements in Range of Mapping
• Equality of Mappings

I

• Identity Mapping is Left Identity
• Identity Mapping is Right Identity
• Image is Subset of Codomain
• Image of Domain is Subset of Codomain
• Image of Preimage of Mapping
• Image of Preimage of Mapping/Corollary
• Image of Subset is Image of Restriction
• Induced Equivalence is an Equivalence Relation
• Induced Group
• Induced Ring
• Induced Structure Associative
• Induced Structure Commutative
• Induced Structure Distributive

I cont.

• Induced Structure Identity
• Induced Structure Inverse
• Injection Induces Total Ordering
• Injection Induces Well-Ordering
• Isomorphism to Closed Interval

M

• Mapping Image of Intersection
• Mapping Image of Set Difference
• Mapping Image of Set Difference/Corollary 1
• Mapping Image of Set Difference/Corollary 2
• Mapping Image of Union
• Mapping Induces Partition on Domain
• Mapping on Increasing Union
• Mapping Preimage of Intersection
• Mapping Preimage of Set Difference
• Mapping Preimage of Set Difference/Corollary 1
• Mapping Preimage of Set Difference/Corollary 2
• Mapping Preimage of Union
• Mappings Partially Ordered by Extension

N

• Natural Number Functions are Uncountable
• Null Mapping

O

• Order Monomorphism into Image is Isomorphism

O cont.

• Ordering Induced by Injection is Ordering

P

• Preimage of Composite Mapping
• Preimage of Cover is Cover
• Preimage of Mapping equals Domain

Q

• Quotient Theorem for Sets

R

• Renaming Mapping is Well-Defined
• Restriction of Mapping is Mapping

S

• Set of All Mappings is a Monoid
• Strictly Decreasing Mapping is Decreasing
• Strictly Increasing Mapping is Increasing
• Strictly Monotone Mapping is Monotone
• Structure Induced by Ring Operations is a Ring
• Structure Induced on Group is Group
• Subset Maps to Subset
• Subset of Codomain is Superset of Image of Preimage
• Subset of Domain is Subset of Preimage of Image
• Subset of Image
• Subset of Preimage
• Subset of Set with Propositional Function
• Sum of Positive and Negative Parts

U

• Union of Disjoint Mappings