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Submanifold

In mathematics, a submanifold of a manifold M {\displaystyle M} is a subset S {\displaystyle S} which itself has the structure of a manifold, and for which the inclusion map S → M {\displaystyle S\rightarrow M} satisfies certain properties. There are different types of submanifolds depending on exactly which properties are required. Different authors…

Formal definition, Properties & Submanifolds of real coordinate space

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Overview

Formal definition

Properties

Submanifolds of real coordinate space

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Map overview Semantic statistics

Submanifold

Nodes43
Edges42
Triples22
Avg. degree1.95
Density0.046512
Components1

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Submanifold

Top relations

related to Properties · 7
Submanifold → Closed, Conversely, Given, If, Suppose, The, This
related to Other variations · 6
Submanifold → An, Counterexamples, Many, Sharpe, There, These
related to Embedded submanifolds · 3
Submanifold → An, Given, That
related to Submanifolds of real coordinate space · 3
Submanifold → Smooth, This, Whitney
related to Immersed submanifolds · 2
Submanifold → An, More
is a · 1
Submanifold → manifold whose boundary agrees with the boundary of the entire manifold

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Important terminology

displaystyle embedded immersed submanifolds map inclusion manifold rightarrow closed isbn subset structure also properties mathematics image immersion injective topology embedding

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Submanifoldis amanifold whose boundary agrees with the boundary of the entire manifold0.90text
Submanifoldrelated to Embedded submanifoldsAn0.60section
Submanifoldrelated to Embedded submanifoldsThat0.60section
Submanifoldrelated to Embedded submanifoldsGiven0.60section
Submanifoldrelated to Immersed submanifoldsAn0.60section
Submanifoldrelated to Immersed submanifoldsMore0.60section
Submanifoldrelated to Other variationsThere0.60section
Submanifoldrelated to Other variationsSharpe0.60section
Submanifoldrelated to Other variationsMany0.60section
Submanifoldrelated to Other variationsThese0.60section
Submanifoldrelated to Other variationsAn0.60section
Submanifoldrelated to Other variationsCounterexamples0.60section

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    Min side: 3
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