Category:Relation Theory

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This category contains results about Relation Theory.
Definitions specific to this category can be found in Definitions/Relation Theory.

Relation theory is the subfield of set theory concerned with the properties of relations and relational structures.

As a relation has the same conceptual definition as a (graph-theoretical) graph, it follows that there is considerable overlap between the fields of relation theory and graph theory.

Subcategories

This category has the following 52 subcategories, out of 52 total.

A

Approximating Relations‎ (10 P)
Auxiliary Relations‎ (21 P)

C

Circular Relations‎ (3 P)
Codomains (Relation Theory)‎ (empty)
Compatible Relations‎ (7 C, 34 P)
Composite Relations‎ (1 C, 29 P)
Connected Relations‎ (1 C, 6 P)
Cross-Relations‎ (1 C, 7 P)

E

Equivalence Relations‎ (19 C, 53 P)
Euclidean Relations‎ (1 P)
Examples of Relations‎ (2 C, 5 P)

G

Graph Theory‎ (59 C, 42 P)

I

Idempotence‎ (6 C, 25 P)
Image of Intersection under Relation‎ (3 P)
Image of Set Difference under Relation‎ (3 P)
Image of Union under Relation‎ (3 P)
Images‎ (7 C, 25 P)
Induced Mappings‎ (2 C)
Inverse Relations‎ (4 C, 44 P)
Inverses of Mappings‎ (empty)

L

Lattice Theory‎ (23 C, 28 P)
Left-Total Relations‎ (1 C, 5 P)
Logical Matrices‎ (1 C)

M

Many-to-One Relations‎ (1 P)
Mapping Theory‎ (74 C, 48 P)
Membership Relation‎ (3 P)

O

One-to-Many Relations‎ (2 C, 2 P)
One-to-One Relations‎ (1 C)
Order Theory‎ (99 C, 140 P)

P

Preimages‎ (5 C)
Preimages under Relations‎ (1 C, 5 P)
Preorder Theory‎ (3 C, 22 P)

R

Reflexive Closures‎ (1 C, 14 P)
Reflexive Reductions‎ (2 C, 8 P)
Reflexive Relations‎ (14 C, 31 P)
Relation Isomorphisms‎ (14 P)
Relational Closures‎ (6 P)
Relational Structures‎ (empty)
Relations‎ (3 C, 10 P)
Restrictions‎ (3 C, 41 P)
Right-Total Relations‎ (5 P)

S

Schröder Rule‎ (3 P)
Serial Relations‎ (6 P)
Symmetric Closures‎ (1 C, 7 P)
Symmetric Relations‎ (10 C, 33 P)

T

Total Relations‎ (1 C, 4 P)
Transitive Closures‎ (3 C, 10 P)
Transitive Relations‎ (12 C, 35 P)
Trichotomies‎ (2 P)
Trivial Relation‎ (1 C, 7 P)

W

Well-Defined Relations‎ (2 P)
Well-Founded Relations‎ (5 C, 18 P)

Pages in category "Relation Theory"

The following 47 pages are in this category, out of 47 total.

B

Binary Relation is Subclass of Product of Domain with Range

C

D

Domain of Relation is Image of Inverse Relation

E

I

L

Loop-Digraph as a Relation

M

P

R

S

U

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