Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X is a connected set if it is a connected space when viewed as a subspace of X. Some related but stronger conditions are path connected, simply connected, and n-connected. Another related notion is locally connected, which neither implies nor follows from connectedness.
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0-Connected0-connectedArc-connectedArc-connected spaceArc ComponentArc connectedArc connected spaceArcwise-connectedArcwise connectedConnected (topology)Connected component (topology)Connected setConnected set in a topological spaceConnected surfaceConnected topologyConnectedness (topology)Connex setDisconnected (topology)Disconnected setDisconnected spaceLocal path connectednessLocally path-connected spaceLocally pathwise-connectedMain theorem of connectednessPath-connectedPath-connected componentPath-connected spacePath-connected topological spacePath-connectednessPath componentPath connectedPath connected spacePath connectednessPathwise-connectedPathwise connectedPathwise connected spaceTotally separatedTotally separated space
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(G,X)-manifold0-Connected0-connected2-group3-manifold3-sphere3D rotation groupAbelian varietyAbstract analytic number theoryAdjoint representationAlbanese varietyAlexandre EremenkoAlgebraic curveAlgebraic groupAmoeba (mathematics)Analytic Fredholm theoremAnalytic continuationAnalytic functionAnalyticity of holomorphic functionsAnna MullikinAntiderivative (complex analysis)Antiholomorphic functionAphelion (software)Arc-connectedArc-connected spaceArc ComponentArc connectedArc connected spaceArcwise-connectedArcwise connectedArens squareArf invariantArrangement (space partition)Arrangement of linesAspherical spaceBalanced setBanach bundleBanach manifoldBanach–Tarski paradoxBarratt–Priddy theorem
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Connected space
In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological space X is a connected set if it is a connected space when viewed as a subspace of X. Some related but stronger conditions are path connected, simply connected, and n-connected. Another related notion is locally connected, which neither implies nor follows from connectedness.
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Dalam topologi dan cabang-caba ...... mengikuti dari keterhubungan.
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Em topologia e ramos relaciona ...... fechado com então é desconexo.
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En topologio, koneksa spaco es ...... subarojn de malplena komunaĵo.
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Ett sammanhängande rum är inom ...... till det ursprungliga rummet.
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In de topologie, een deelgebie ...... lisen waartussen "ruimte" zit.
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In der mathematischen Topologi ...... heißt Zusammenhangskomponente.
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In matematica uno spazio topol ...... i "pezzi" da cui è formato X.
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In topology and related branch ...... or follows from connectedness.
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La connexité est une notion de ...... nte connexe de l'objet étudié.
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Przestrzeń spójna – przestrzeń ...... podprzestrzeń tej przestrzeni.
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1,020,369,546
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right
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author
V. I. Malykhin
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caption
From top to bottom: red space ...... has genus 1 and D has genus 4.
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vertical
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header
Connected and disconnected subspaces of R²
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image
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left
true
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title
Connected Set
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Connected space
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Proof
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urlname
ConnectedSet
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comment
Dalam topologi dan cabang-caba ...... ihat sebagai subruang dari X'.
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Em topologia e ramos relaciona ...... caso dizemos que é desconexo.
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En topologio, koneksa spaco es ...... subarojn de malplena komunaĵo.
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Ett sammanhängande rum är inom ...... till det ursprungliga rummet.
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In de topologie, een deelgebie ...... lisen waartussen "ruimte" zit.
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In der mathematischen Topologi ...... heißt Zusammenhangskomponente.
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In matematica uno spazio topol ...... sificare gli spazi topologici.
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In topology and related branch ...... or follows from connectedness.
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La connexité est une notion de ...... nte connexe de l'objet étudié.
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Przestrzeń spójna – przestrzeń ...... podprzestrzeń tej przestrzeni.
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Conjunt connex
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Conjunto conexo
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Connected space
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Connexité (mathématiques)
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Espaço conexo
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Koneksa spaco
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Przestrzeń spójna
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Ruang terhubung
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Samenhang
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Sammanhängande rum
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