Category:Definitions/Order Theory
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This category contains definitions related to Order Theory.
Related results can be found in Category:Order Theory.
Order theory is the branch of relation theory which studies orderings.
Subcategories
This category has the following 73 subcategories, out of 73 total.
A
B
C
- Definitions/Comparable Sets (5 P)
D
- Definitions/Decreasing Sequences (16 P)
- Definitions/Dedekind Cuts (7 P)
- Definitions/Densely Ordered (6 P)
- Definitions/Dual Orderings (6 P)
E
F
G
I
- Ideals (Order Theory) (empty)
- Definitions/Increasing Sequences (19 P)
- Definitions/Infima (27 P)
- Definitions/Initial Segments (5 P)
L
- Definitions/Lower Sections (8 P)
M
- Definitions/Max Operation (3 P)
- Definitions/Maximal Elements (11 P)
- Definitions/Min Operation (2 P)
- Definitions/Minimal Elements (8 P)
N
- Definitions/Negative Numbers (2 P)
O
- Definitions/Order Isomorphisms (18 P)
- Definitions/Order Sums (3 P)
- Definitions/Order Types (5 P)
- Definitions/Ordered Geometry (1 P)
- Definitions/Ordered Sums (3 P)
P
- Definitions/Predecessor Elements (16 P)
R
S
- Definitions/Smallest Elements (11 P)
- Definitions/Successor Elements (12 P)
- Definitions/Suprema (34 P)
T
U
- Definitions/Upper Sections (5 P)
W
Pages in category "Definitions/Order Theory"
The following 200 pages are in this category, out of 232 total.
(previous page) (next page)A
- User:Abcxyz/Sandbox/Dedekind Completions of Ordered Sets
- Definition:Algebraic Ordered Set
- Definition:Antilexicographic Order
- Definition:Approximating Relation
- Definition:Archimedean Property/Ordering
- Definition:Arithmetic Ordered Set
- Definition:Ascending Chain Condition
- Definition:Auxiliary Relation
C
- Definition:Category of Ordered Sets
- Definition:Chain (Order Theory)
- Definition:Chain (Order Theory)/Subset Relation
- Definition:Chain Complete Set
- Definition:Closed under Directed Suprema
- Definition:Closure System
- Definition:Compact Closure
- Definition:Compact Element
- Definition:Comparable Sets
- Definition:Comparable Sets/Subset Ordering
- Definition:Completely Irreducible
- Definition:Completely Prime Filter
- Definition:Completely Prime Ideal
- Definition:Continuous Lattice Subframe
- Definition:Continuous Ordered Set
- Definition:Convex Set (Order Theory)
- Definition:Cut (Analysis)
D
- Definition:Decreasing
- Definition:Dedekind Completeness Property
- Definition:Dedekind Completion
- Definition:Dedekind Cut
- Definition:Dedekind-MacNeille Completion
- Definition:Dense
- Definition:Densely Ordered
- User:Dfeuer/Definition:Positive Cone
- User:Dfeuer/Definition:Strict Total Positive Cone
- User:Dfeuer/Definition:Strictly Positive Cone
- User:Dfeuer/Definition:Total Positive Cone
- Definition:Directed Ordering
- Definition:Directed Suprema Inheriting
- Definition:Distributive Lattice
- Definition:Dual Isomorphism (Order Theory)
- Definition:Dual Ordering
- Definition:Dual Statement (Order Theory)
E
G
- Definition:G-Ordered Class
- Definition:Galois Connection
- Definition:Generator Set of Filter
- Definition:Greater Than
- Definition:Greatest
- Definition:Greatest Element
- Definition:Greatest Element of Subset
- Definition:Greatest Element/Subset
- Definition:Greatest Set by Set Inclusion
- Definition:Greatest Set by Set Inclusion (Class Theory)
- Definition:Greatest Set by Set Inclusion/Class Theory
I
- Definition:Ideal (Order Theory)
- Definition:Ideal (Order Theory)/Proper Ideal
- Definition:Inaccessible by Directed Suprema
- Definition:Inclusion Ordered Set
- Definition:Increasing
- Definition:Increasing Mappings Satisfying Inclusion in Lower Closure
- Definition:Inductive Ordered Set
- Definition:Inequality
- Definition:Infima Inheriting
- Definition:Inflationary Mapping
- Definition:Initial Segment
- Definition:Interval/Ordered Set
- Definition:Inverse Ordered Set
- Definition:Inverse Ordering
L
M
- Definition:Max Operation
- Definition:Max Operation (General Case)
- Definition:Maximal
- Definition:Maximal Set
- Definition:Maximal/Element
- Definition:Maximal/Set
- Definition:Meet (Order Theory)
- Definition:Meet Closed
- Definition:Meet Irreducible
- Definition:Meet-Continuous Lattice
- Definition:Min Operation
- Definition:Min Operation (General Case)
- Definition:Minimal
- Definition:Minimal Condition/Ordered Set
- Definition:Minimal Set
- Definition:Minimal Uncountable Well-Ordered Set
- Definition:Minimal/Element
- Definition:Minimal/Set
- Definition:Monotone (Order Theory)
- Definition:Monotone (Order Theory)/Mapping
- Definition:Monotone (Order Theory)/Sequence
- Definition:Monotone (Order Theory)/Sequence/Real Sequence
- Definition:Monotone Mapping
- Definition:Monotone Sequence
- Definition:Monotonicity
- Definition:Multiplicative Relation
N
O
- Definition:Order Complete Set
- Definition:Order Completion
- Definition:Order Embedding
- Definition:Order Isomorphism
- Definition:Order Product
- Definition:Order Sum
- Definition:Order Theory
- Definition:Order Type
- Definition:Order-Preserving
- Definition:Order-Preserving Mapping
- Definition:Order-Reflecting Mapping
- Definition:Ordered Class
- Definition:Ordered Set
- Definition:Ordered Set of All Mappings
- Definition:Ordered Set of Closure Operators
- Definition:Ordered Set of Closure Systems
- Definition:Ordered Set of Increasing Mappings
- Definition:Ordered Set of Subalgebras
- Definition:Ordered Structure
- Definition:Ordered Sum
- Definition:Ordered Sum/General Definition
- Definition:Ordering
- Definition:Ordering by Reverse Inclusion
- Definition:Ordering Induced by Injection
- Definition:Ordering Induced by Positivity Property
- Definition:Ordering Induced by Preordering
- Definition:Ordering on Extended Real Numbers
- Definition:Ordering on Integers
- Definition:Ordering on Mappings
- Definition:Ordinal
P
- Definition:Partial Ordering
- Definition:Partially Ordered Set
- Definition:Pointwise Inequality
- Definition:Pointwise Inequality of Extended Real-Valued Functions
- Definition:Pointwise Inequality of Real-Valued Functions
- Definition:Positive
- Definition:Positive Real Number
- Definition:Positive/Integer
- Definition:Positive/Number
- Definition:Positive/Real Number
- Definition:Positively Totally Ordered Semigroup
- Definition:Positivity Property
- Definition:Precede
- Definition:Prime Element (Order Theory)
- Definition:Prime Filter (Order Theory)
- Definition:Prime Ideal (Order Theory)
- Definition:Proper Ideal (Order Theory)
- Definition:Property (S)
S
- Definition:Scott Sigma
- Definition:Self-Dual (Order Theory)
- Definition:Set Ordered by Inclusion
- Definition:Set Ordered by Subset Relation
- Definition:Set Ordered by Subset Relation/Reverse Inclusion
- Definition:Simple Order Product
- Definition:Smallest
- Definition:Smallest Element
- Definition:Smallest Element/Subset
- Definition:Smallest Set by Set Inclusion
- Definition:Smallest Set by Set Inclusion (Class Theory)
- Definition:Smallest Set by Set Inclusion/Class Theory
- Definition:Strict Down-Set
- Definition:Strict Initial Segment
- Definition:Strict Lower Set
- Definition:Strict Ordering
- Definition:Strict Weak Ordering
- Definition:Strictly Between
- Definition:Strictly Monotone
- Definition:Strictly Monotone Mapping
- Definition:Strictly Monotone Sequence
- Definition:Strictly Monotone/Sequence
- Definition:Strictly Monotone/Sequence/Real Sequence
- Definition:Strictly Negative
- Definition:Strictly Negative Integer
- Definition:Strictly Negative Real Number
- Definition:Strictly Negative/Integer
- Definition:Strictly Negative/Number
- Definition:Strictly Negative/Real Number
- Definition:Strictly Ordered Set
- Definition:Strictly Positive