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Specialization preorder

In the branch of mathematics known as topology, the specialization (or canonical) preorder is a natural preorder on the set of the points of a topological space. For most spaces that are considered in practice, namely for all those that satisfy the T0 separation axiom, this preorder is even a partial order (called the specialization order). On the other…

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Overview

Definition and motivation

Upper and lower sets

Examples

Important properties

Topologies on orders

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Map overview Semantic statistics

Specialization preorder

Nodes68
Edges67
Triples22
Avg. degree1.97
Density0.029412
Components1

How this topic connects Entity context

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Specialization preorder

Top relations

related to Important properties · 6
Specialization preorder → As, In, T0, That, The, Therefore
related to Upper and lower sets · 6
Specialization preorder → Alexandrov-discrete, Every, For, In, Let, The
related to Topologies on orders · 5
Specialization preorder → Indeed, Is, It, The, The Alexandroff
related to Definition and motivation · 4
Specialization preorder → Consider, However, The, What
is a · 1
Specialization preorder → preorder

Important terminology Word statistics

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Important terminology

specialization order sets topology space preorder open displaystyle closed set topological spaces upper one every sober also topologies t0 points

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Specialization preorderis apreorder0.90text
Specialization preorderrelated to Definition and motivationConsider0.60section
Specialization preorderrelated to Definition and motivationThe0.60section
Specialization preorderrelated to Definition and motivationHowever0.60section
Specialization preorderrelated to Definition and motivationWhat0.60section
Specialization preorderrelated to Important propertiesAs0.60section
Specialization preorderrelated to Important propertiesThe0.60section
Specialization preorderrelated to Important propertiesThat0.60section
Specialization preorderrelated to Important propertiesTherefore0.60section
Specialization preorderrelated to Important propertiesT00.60section
Specialization preorderrelated to Important propertiesIn0.60section
Specialization preorderrelated to Topologies on ordersThe0.60section

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    Min side: 3
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