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Cocountable topology

The cocountable topology, also known as the countable complement topology, is a topology that can be defined on any infinite set X {\displaystyle X} . In this topology, a set is open if its complement in X {\displaystyle X} is either countable or equal to the entire set. Equivalently, the open sets consist of the empty set and all subsets of X…

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Properties

LindelöfT1IntersectHausdorffCompact sets
12 related topics

Definitions

SubsetsTopological spaceUncountable setEuclidean topology
4 related topics

Examples

Standard topologyMetrizableSubspace topology
3 related topics

Proof that cocountable topology is a topology

VacuouslyDe Morgan's laws
2 related topics

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Overview

Definitions

Proof that cocountable topology is a topology

Properties

Examples

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Map overview Semantic statistics

Cocountable topology

Nodes34
Edges33
Triples21
Avg. degree1.94
Density0.058824
Components1

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Cocountable topology

Top relations

related to Properties · 8
Cocountable topology → Every, Hausdorff, However, If, It, Lindelöf, Since, T1
related to Examples · 7
Cocountable topology → Countable, Hausdorff, If, In, On, T1, Uncountable
related to Cocountable extension topology · 4
Cocountable topology → Euclidean, Let, Now, The
is a · 2
Cocountable topology → proper subset of the standard topology, topologyBy definition

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Important terminology

displaystyle topology countable set mathcal cocountable complement setminus sets open subsets also since empty varnothing subseteq uncountable closed known hausdorff

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cocountable topologyis atopologyBy definition0.90text
Cocountable topologyis aproper subset of the standard topology0.90text
Cocountable topologyrelated to Cocountable extension topologyLet0.60section
Cocountable topologyrelated to Cocountable extension topologyNow0.60section
Cocountable topologyrelated to Cocountable extension topologyEuclidean0.60section
Cocountable topologyrelated to Cocountable extension topologyThe0.60section
Cocountable topologyrelated to ExamplesUncountable0.60section
Cocountable topologyrelated to ExamplesOn0.60section
Cocountable topologyrelated to ExamplesIn0.60section
Cocountable topologyrelated to ExamplesT10.60section
Cocountable topologyrelated to ExamplesHausdorff0.60section
Cocountable topologyrelated to ExamplesCountable0.60section

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