Open Set -- from Wolfram MathWorld

. In one-space, the open set is an open interval. In two-space, the open set is a disk. In three-space, ... Algebra AppliedMathematics CalculusandAnalysis DiscreteMathematics FoundationsofMathematics Geometry HistoryandTerminology NumberTheory ProbabilityandStatistics RecreationalMathematics Topology AlphabeticalIndex NewinMathWorld Topology Point-SetTopology OpenSet Letbeasubsetofametric space.Thenthesetisopenifevery pointinhasaneighborhood lyingintheset.Anopensetofradiusandcenteristhesetofallpointssuchthat,andisdenoted.Inone-space, theopensetisanopeninterval.Intwo-space, theopensetisadisk.Inthree-space,theopensetis aball. Moregenerally,givenatopology(consistingofasetandacollectionofsubsets),asetissaidtobeopenifitis in.Therefore,whileitisnotpossibleforaset tobebothfiniteandopeninthetopologyoftherealline(asinglepointisaclosed set),itispossibleforamoregeneraltopologicalset tobebothfiniteandopen. Thecomplementofanopensetisaclosedset.Itispossibleforasettobeneitheropennorclosed,e.g., thehalf-closedinterval. SeealsoBall,BorelSet,ClosedSet,EmptySet, Neighborhood,OpenBall, OpenDisk,OpenInterval, OpenNeighborhoodExplorethistopicintheMathWorldclassroom ExplorewithWolfram|Alpha Morethingstotry: 15.25+7.90+3.12 exp(z)limitrepresentation JacobiDN(EllipticK(k),k) ReferencesCroft,H. T.;Falconer,K. J.;andGuy,R. K.Unsolved ProblemsinGeometry.NewYork:Springer-Verlag,p. 2,1991.Krantz, S. G.Handbook ofComplexVariables.Boston,MA:Birkhäuser,p. 3,1999.Referenced onWolfram|AlphaOpenSet Citethisas: Weisstein,EricW."OpenSet."FromMathWorld--AWolframWebResource.https://mathworld.wolfram.com/OpenSet.html Subjectclassifications Topology Point-SetTopology Created,developedandnurturedbyEricWeissteinatWolframResearch