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Closed point

In mathematics, a closed point of a topological space is a point whose singleton is closed. In many areas of geometry and topology, all spaces under consideration are T1 spaces that only have closed points. The distinction between closed and non-closed points is most often made in algebraic geometry, where schemes can have non-closed points.

Examples, Properties & Definition and motivation

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Explore the main themes, entities and connections around Closed point. Start with the topic map, then use the sections below for research and deeper semantic analysis.

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Overview

Definition and motivation

Examples

Properties

Locally closed point

Advanced semantic analysis

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Map overview Semantic statistics

Closed point

Nodes67
Edges66
Triples28
Avg. degree1.97
Density0.029851
Components1

How this topic connects Entity context

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Closed point

Top relations

related to Examples · 13
Closed point → Alexandrov, Hausdorff, If, In, Most, One, Other, T1, The, The Sierpiński, This, When, Zariski-closed
related to Properties · 6
Closed point → For, However, In, Nonempty, Sierpiński, This
related to Definition and motivation · 5
Closed point → An, Given, If, The, This
related to Locally closed point · 4
Closed point → Every, Goldman, This, Unlike

Important terminology Word statistics

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Important terminology

closed points displaystyle scheme point space schemes spaces locally t1 overline every particular non-closed algebraic geometry spectrum field normal affine

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Closed pointrelated to Definition and motivationIf0.60section
Closed pointrelated to Definition and motivationAn0.60section
Closed pointrelated to Definition and motivationThe0.60section
Closed pointrelated to Definition and motivationGiven0.60section
Closed pointrelated to Definition and motivationThis0.60section
Closed pointrelated to ExamplesMost0.60section
Closed pointrelated to ExamplesHausdorff0.60section
Closed pointrelated to ExamplesT10.60section
Closed pointrelated to ExamplesThis0.60section
Closed pointrelated to ExamplesOther0.60section
Closed pointrelated to ExamplesWhen0.60section
Closed pointrelated to ExamplesZariski-closed0.60section

Related concept clusters Concept neighborhoods

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    Connections between topic areas Semantic bridges

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    Min side: 3
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