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Inductive dimension

In the mathematical field of topology, the inductive dimension of a topological space X is either of two values, the small inductive dimension ind(X) or the large inductive dimension Ind(X). These are based on the observation that, in n-dimensional Euclidean space Rn, the boundaries of balls have dimension n − 1. Therefore it should be possible to define…

Relationships between dimensions, Formal definitions & Examples

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Relationships between dimensions

Normal spaceCountable baseSeparableMetrizableUrysohn's metrization theorem
11 related topics

Formal definitions

ClosureSubspace topologyClosed
3 related topics

Examples

Irrational numbers
1 related topics

Overview

TopologyTopological spaceEuclidean spaceBoundariesBalls
9 related topics

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Formal definitions

Examples

Relationships between dimensions

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Map overview Semantic statistics

Inductive dimension

Nodes29
Edges28
Triples47
Avg. degree1.93
Density0.068966
Components1

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Inductive dimension

Top relations

related to Further reading · 35
Inductive dimension → Arkhangel'skii, Berlin ISBN, Cambridge University Press, Crilly, Dimension, Dimension Theory, Dimensions, Dokl, Eds, Elsevier, Encyclopaedia, Engelking, Fedorchuk, Filippov, Finite, General Topology, Grattan-Guinness, Heldermann Verlag, Infinite, ISBN
related to Examples · 6
Inductive dimension → Both, Consider, Euclidean, For, Intuitively, R3
related to Formal definitions · 6
Inductive dimension → Euclidean, Here, If, In, Then, We

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Important terminology

dimension space inductive dimensions ind topology topological spaces displaystyle euclidean small large boundary open two lebesgue covering boundaries nöbeling theory

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Inductive dimensionrelated to ExamplesFor0.60section
Inductive dimensionrelated to ExamplesConsider0.60section
Inductive dimensionrelated to ExamplesEuclidean0.60section
Inductive dimensionrelated to ExamplesR30.60section
Inductive dimensionrelated to ExamplesIntuitively0.60section
Inductive dimensionrelated to ExamplesBoth0.60section
Inductive dimensionrelated to Formal definitionsWe0.60section
Inductive dimensionrelated to Formal definitionsThen0.60section
Inductive dimensionrelated to Formal definitionsHere0.60section
Inductive dimensionrelated to Formal definitionsIn0.60section
Inductive dimensionrelated to Formal definitionsEuclidean0.60section
Inductive dimensionrelated to Formal definitionsIf0.60section

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