Clopen set
In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible may seem counter-intuitive, as the common meanings of open and closed are antonyms, but their mathematical definitions are not mutually exclusive. A set is closed if its complement is open, which leaves the possibility of an open set whose complement is also open, making both sets both open and closed, and therefore clopen.
Appert topologyAxiom of determinacyBoolean algebra (structure)Boolean algebras canonically definedBoundary (topology)Cantor algebraCantor setCantor spaceClopenClopen setsClopen subsetClosed-openClosed-open setClosed and openClosed setClosure (mathematics)Closure (topology)Connected spaceCylinder setDeterminacyDiscrete spaceDistributive latticeDuality theory for distributive latticesEmpty setEsakia dualityEsakia spaceEuclid's theoremExtension topologyField of setsFinite topological spaceFree Boolean algebraFurstenberg's proof of the infinitude of primesGeneral frameGeneral topologyGlossary of topologyHalf-openIdeal (order theory)Identity componentInterior algebraIrrational number
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Clopen set
In topology, a clopen set (a portmanteau of closed-open set) in a topological space is a set which is both open and closed. That this is possible may seem counter-intuitive, as the common meanings of open and closed are antonyms, but their mathematical definitions are not mutually exclusive. A set is closed if its complement is open, which leaves the possibility of an open set whose complement is also open, making both sets both open and closed, and therefore clopen.
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En topologia, un conjunt obert ...... que és alhora obert i tancat.
@ca
En topologie, un ouvert-fermé ...... mplémentaire est aussi ouvert.
@fr
En topología, un conjunto clop ...... es a la vez abierto y cerrado.
@es
In de topologie, een onderdeel ...... ant van deze term is geslopen.
@nl
In topologia, un insieme chius ...... mporaneamente aperto e chiuso.
@it
In topology, a clopen set (a p ...... closed, and therefore clopen.
@en
Obojetná množina (anglicky clo ...... avřené, a proto jsou obojetné.
@cs
Zbiór otwarto-domknięty – podz ...... zbiorem otwartym i domkniętym.
@pl
Відкрито-замкнута множина — пі ...... одночас відкритою і замкнутою.
@uk
在拓扑学中，在拓扑空间中的闭开集（Clopen set）是既是开集又是闭集的集合。
@zh
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En topologia, un conjunt obert ...... que és alhora obert i tancat.
@ca
En topologie, un ouvert-fermé ...... mplémentaire est aussi ouvert.
@fr
En topología, un conjunto clop ...... es a la vez abierto y cerrado.
@es
In de topologie, een onderdeel ...... ant van deze term is geslopen.
@nl
In topologia, un insieme chius ...... mporaneamente aperto e chiuso.
@it
In topology, a clopen set (a p ...... closed, and therefore clopen.
@en
Obojetná množina (anglicky clo ...... avřené, a proto jsou obojetné.
@cs
Zbiór otwarto-domknięty – podz ...... zbiorem otwartym i domkniętym.
@pl
Відкрито-замкнута множина — пі ...... одночас відкритою і замкнутою.
@uk
在拓扑学中，在拓扑空间中的闭开集（Clopen set）是既是开集又是闭集的集合。
@zh
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Abgeschlossene offene Menge
@de
Clopen set
@en
Clopen verzameling
@nl
Conjunt clopen
@ca
Conjunto clopen
@es
Fermito-malfermita aro
@eo
Insieme chiuso-aperto
@it
Obojetná množina
@cs
Ouvert-fermé
@fr
Zbiór otwarto-domknięty
@pl