Topological manifold

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Examples

Discrete space Circle Compact Torus Klein bottle

22 related topics

Properties

Local homeomorphisms Topological property Locally compact Locally connected First countable

27 related topics

Classification of manifolds

Sphere Connected sum Projective planes Thurston's geometrization conjecture Grigori Perelman

11 related topics

Coordinate charts

Open ball Basis Covered Atlas Cartography

9 related topics

Topics to explore

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Overview

Topology
Topological space
Real Real numbers
Dimensional Dimension (mathematics)
Euclidean space
Manifolds Manifold
Differentiable manifolds Differentiable manifold
Differential structure
E8 manifold

Formal definition

Examples

Discrete space
Circle
Compact Compact space
Torus
Klein bottle
Surfaces Surface (topology)
N-dimensional sphere N-sphere
N-dimensional torus N-torus
Projective spaces Projective space
Reals Real number
Complexes Complex number
Quaternions Quaternion
Real projective space
Complex projective space
Quaternionic projective space
Grassmannians Grassmannian
Flag manifolds Flag manifold
Stiefel manifolds Stiefel manifold
Lens spaces Lens space
Quotients Quotient space (topology)
Lie groups Lie group
Group Group (mathematics)

Properties

Local homeomorphisms Local homeomorphism
Topological property
Locally compact Locally compact space
Locally connected Locally connected space
First countable First-countable space
Locally contractible Locally contractible space
Locally metrizable Locally metrizable space
Tychonoff spaces Tychonoff space
Σ-compactness Σ-compact
Disjoint union Disjoint union (topology)
Connected components Connected component (topology)
If and only if
Not be Non-Hausdorff manifold
T1 T1 space
Line with two origins
Metrizable Metrizable space
Long line Long line (topology)
Normal Normal space
Pathological Pathological (mathematics)
Perfectly normal Hausdorff spaces Perfectly normal Hausdorff space
Second-countable Second-countable space
Embeds Embedding
Lindelöf Lindelöf space
Σ-compact Σ-compact space
Countable Countable set
Separable Separable space
Invariance of domain

Coordinate charts

Open ball
Basis Basis (topology)
Covered Cover (topology)
Atlas Atlas (topology)
Cartography
Globe
Atlas
Differentiable manifolds
Smooth Diffeomorphism

Classification of manifolds

Sphere
Connected sum
Projective planes Real projective plane
Thurston's geometrization conjecture
Grigori Perelman
Word problem Word problem for groups
Group theory
Algorithmically undecidable Undecidable problem
Algorithm
Simply connected
Half-space Half-space (geometry)

Constructions

Advanced semantic analysis

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Map overview Semantic statistics

Nodes98

Edges97

Triples51

Avg. degree1.98

Density0.020408

Components1

How this topic connects Entity context

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Topological manifold

Top relations

related to References · 26

Topological manifold → America, Foundational Essays, Gauld, Graduate Texts, Introduction, ISBN, John, JSTOR, Kirby, Laurence, Lee, Manifolds, Mathematical Association, Mathematics, New York, PDF, Princeton, Princeton University Press, Robion, Siebenmann

related to Compactness and countability axioms · 10

Topological manifold → Euclidean, For, Hausdorff, In, Lindelöf, Manifolds, Paracompact, Since, The, This

related to Formal definition · 5

Topological manifold → Euclidean, Euclidean Hausdorff, In, It, Rn

related to Other manifolds · 4

Topological manifold → Differentiable, Lens, Lie, The E8

is a · 3

Topological manifold → locally Euclidean Hausdorff space, topological manifold with boundary, topological space that locally resembles real n-dimensional Euclidean space

related to Manifolds with boundary · 3

Topological manifold → Euclidean, Every, Hausdorff

Important terminology Word statistics

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Important terminology

manifold manifolds space topological euclidean locally every hausdorff homeomorphic paracompact second-countable compact structure n-manifold connected open neighborhood differentiable spaces projective

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Topological manifold	is a	topological space that locally resembles real n-dimensional Euclidean space	0.90	text
Topological manifold	is a	locally Euclidean Hausdorff space	0.90	text
Topological manifold	is a	topological manifold with boundary	0.90	text
Topological manifold	related to Compactness and countability axioms	The	0.60	section
Topological manifold	related to Compactness and countability axioms	Hausdorff	0.60	section
Topological manifold	related to Compactness and countability axioms	Since	0.60	section
Topological manifold	related to Compactness and countability axioms	In	0.60	section
Topological manifold	related to Compactness and countability axioms	Paracompact	0.60	section
Topological manifold	related to Compactness and countability axioms	Manifolds	0.60	section
Topological manifold	related to Compactness and countability axioms	This	0.60	section
Topological manifold	related to Compactness and countability axioms	Euclidean	0.60	section
Topological manifold	related to Compactness and countability axioms	For	0.60	section

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Min side: 3

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Examples

Properties

Classification of manifolds

Coordinate charts

Key facts & relationships

Topics to explore

Overview

Formal definition

Examples

Properties

Coordinate charts

Classification of manifolds

Constructions

Advanced semantic analysis

Map overview Semantic statistics

Topological manifold

How this topic connects Entity context

Topological manifold

Top relations

Important terminology Word statistics

Important terminology

Entity relationships Subject–Predicate–Object triples

Related concept clusters Concept neighborhoods

Connections between topic areas Semantic bridges