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- Closed_manifold abstract "In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold.The simplest example is a circle, which is a compact one-dimensional manifold. Other examples of closed manifolds are the torus and the Klein bottle. As a counterexample, the real line is not a closed manifold because it is not compact. A disk is a compact two-dimensional manifold, but is not a closed manifold because it has a boundary. Compact manifolds are, in an intuitive sense, "finite". By the basic properties of compactness, a closed manifold is the disjoint union of a finite number of connected closed manifolds. One of the most basic objectives of geometric topology is to understand what the supply of possible closed manifolds is. All compact topological manifolds can be embedded into for some n, by the Whitney embedding theorem.".
- Closed_manifold wikiPageID "669475".
- Closed_manifold wikiPageRevisionID "591865045".
- Closed_manifold hasPhotoCollection Closed_manifold.
- Closed_manifold subject Category:Geometric_topology.
- Closed_manifold subject Category:Manifolds.
- Closed_manifold type Artifact100021939.
- Closed_manifold type Conduit103089014.
- Closed_manifold type Manifold103717750.
- Closed_manifold type Manifolds.
- Closed_manifold type Object100002684.
- Closed_manifold type Passage103895293.
- Closed_manifold type PhysicalEntity100001930.
- Closed_manifold type Pipe103944672.
- Closed_manifold type Tube104493505.
- Closed_manifold type Way104564698.
- Closed_manifold type Whole100003553.
- Closed_manifold type YagoGeoEntity.
- Closed_manifold type YagoPermanentlyLocatedEntity.
- Closed_manifold comment "In mathematics, a closed manifold is a type of topological space, namely a compact manifold without boundary. In contexts where no boundary is possible, any compact manifold is a closed manifold.The simplest example is a circle, which is a compact one-dimensional manifold. Other examples of closed manifolds are the torus and the Klein bottle. As a counterexample, the real line is not a closed manifold because it is not compact.".
- Closed_manifold label "Closed manifold".
- Closed_manifold label "Geschlossene Mannigfaltigkeit".
- Closed_manifold label "Gesloten variëteit".
- Closed_manifold label "Variedade fechada".
- Closed_manifold label "Замкнутое многообразие".
- Closed_manifold sameAs Geschlossene_Mannigfaltigkeit.
- Closed_manifold sameAs Gesloten_variëteit.
- Closed_manifold sameAs Variedade_fechada.
- Closed_manifold sameAs m.031dt6.
- Closed_manifold sameAs Q1517914.
- Closed_manifold sameAs Q1517914.
- Closed_manifold sameAs Closed_manifold.
- Closed_manifold wasDerivedFrom Closed_manifold?oldid=591865045.
- Closed_manifold isPrimaryTopicOf Closed_manifold.