Star domain
In geometry, a setin the Euclidean spaceis called a star domain (or star-convex set, star-shaped set[1] or radially convex set) if there exists anthe line segment fromThis definition is immediately generalizable to any real, or complex, vector space.Intuitively, if one thinks ofas a region surrounded by a wall,is a star domain if one can find a vantage pointA similar, but distinct, concept is that of a radial set.in a vector space(such as Euclidean space), the convex hull ofis called the closed interval with endpointsthe closed intervalis star shaped and is called a star domain if there exists some pointA set that is star-shaped at the origin is sometimes called a star set.[2] Such sets are closely related to Minkowski functionals.
StarshapedconvexannulusgeometryEuclidean spaceline segmentcomplexvector spaceradial setconvex hullMinkowski functionalsstar-shaped polygonnon-emptyconvex setclosureinteriorcontractiblesimply connectedintersectionunit lengthbalanced setdiffeomorphicAbsolutely convex setAbsorbing setArt gallery problemBounded set (topological vector space)Minkowski functionalStar polygonSymmetric setStar-shaped preferencesAmerican Mathematical MonthlyRudin, WalterMcGraw-Hill Science/Engineering/MathSchaefer, Helmut H.Schechter, EricMathWorldFunctional analysistopicsglossaryBanachFréchetHilbertHölderNuclearOrliczSchwartzSobolevTopological vectorBarrelledCompleteLocally convexReflexiveSeparableHahn–BanachRiesz representationClosed graphUniform boundedness principleKrein–MilmanMin–maxGelfand–NaimarkBanach–AlaogluAdjointBoundedCompactHilbert–SchmidtNormalTrace classTransposeUnboundedUnitaryBanach algebraC*-algebraSpectrum of a C*-algebraOperator algebraGroup algebra of a locally compact groupVon Neumann algebraInvariant subspace problemMahler's conjectureHardy spaceSpectral theory of ordinary differential equationsHeat kernelIndex theoremCalculus of variationsFunctional calculusIntegral linear operatorJones polynomialTopological quantum field theoryNoncommutative geometryRiemann hypothesisDistributionGeneralized functionsApproximation propertyChoquet theoryWeak topologyBanach–Mazur distanceTomita–Takesaki theoryTopological vector spacesBanach spaceCompletenessContinuous linear operatorLinear functionalFréchet spaceLinear mapLocally convex spaceMetrizabilityOperator topologiesTopological vector spaceAnderson–KadecClosed graph theoremF. Riesz'shyperplane separationVector-valued Hahn–BanachOpen mapping (Banach–Schauder)Bounded inverseUniform boundedness (Banach–Steinhaus)Bilinear operatorAlmost openContinuousClosedDensely definedDiscontinuousTopological homomorphismFunctionalLinearBilinearSesquilinear