KnowraIdentity theoremLinked fromLinked fromThe 20 pages that link to Identity theorem, each with the reason it gives.All 20Related 19Compared with 1Holomorphic functionRelated: It captures how local agreement determines a holomorphic function across its domain.Analytic continuationRelated: It guarantees uniqueness when two proposed extensions overlap.Cauchy's integral formulaRelated: The formula’s analytic consequences help make values on a small set determine a whole function.Maximum modulus principleRelated: Once constancy holds near an interior maximum, this theorem extends it across the connected domain.Meromorphic functionRelated: It also constrains meromorphic functions because their holomorphic regions obey the same uniqueness principle.Entire functionRelated: An entire function is fixed globally by its values on any suitable set.Liouville's theoremRelated: It is another holomorphic rigidity result, but its constraint comes from matching values rather than boundedness.Schwarz lemmaRelated: It explains why matching an equality case at a point can force global agreement.Complex differentiabilityRelated: Regional complex differentiability makes values on a small set determine the entire function.Cauchy estimatesRelated: Derivative control supports the local power-series structure behind this uniqueness result.Removable singularityRelated: An extension across one point remains constrained by the function's values nearby.Weierstrass factorization theoremRelated: It helps explain why zero data can strongly constrain an analytic function.Complex derivativeRelated: Complex differentiability helps make values on a small set determine an entire function.Hurwitz's theoremRelated: It underlies the rigidity behind the theorem's identically-zero alternative.Hartogs extension theoremRelated: Uniqueness ensures that any extension across the hole is determined by the original function.Schwarz reflection principleRelated: Uniqueness of the extension follows from agreement on the original domain.Casorati–Weierstrass theoremRelated: It supports uniqueness arguments that rule out a nonconstant function taking only restricted local values.Analytic functionRelated: Local agreement determines the entire analytic function on a connected domain.Analyticity of holomorphic functionsRelated: Local power-series equality makes agreement on a small set determine the function throughout its domain.
KnowraIdentity theoremLinked fromLinked fromThe 20 pages that link to Identity theorem, each with the reason it gives.All 20Related 19Compared with 1Holomorphic functionRelated: It captures how local agreement determines a holomorphic function across its domain.Analytic continuationRelated: It guarantees uniqueness when two proposed extensions overlap.Cauchy's integral formulaRelated: The formula’s analytic consequences help make values on a small set determine a whole function.Maximum modulus principleRelated: Once constancy holds near an interior maximum, this theorem extends it across the connected domain.Meromorphic functionRelated: It also constrains meromorphic functions because their holomorphic regions obey the same uniqueness principle.Entire functionRelated: An entire function is fixed globally by its values on any suitable set.Liouville's theoremRelated: It is another holomorphic rigidity result, but its constraint comes from matching values rather than boundedness.Schwarz lemmaRelated: It explains why matching an equality case at a point can force global agreement.Complex differentiabilityRelated: Regional complex differentiability makes values on a small set determine the entire function.Cauchy estimatesRelated: Derivative control supports the local power-series structure behind this uniqueness result.Removable singularityRelated: An extension across one point remains constrained by the function's values nearby.Weierstrass factorization theoremRelated: It helps explain why zero data can strongly constrain an analytic function.Complex derivativeRelated: Complex differentiability helps make values on a small set determine an entire function.Hurwitz's theoremRelated: It underlies the rigidity behind the theorem's identically-zero alternative.Hartogs extension theoremRelated: Uniqueness ensures that any extension across the hole is determined by the original function.Schwarz reflection principleRelated: Uniqueness of the extension follows from agreement on the original domain.Casorati–Weierstrass theoremRelated: It supports uniqueness arguments that rule out a nonconstant function taking only restricted local values.Analytic functionRelated: Local agreement determines the entire analytic function on a connected domain.Analyticity of holomorphic functionsRelated: Local power-series equality makes agreement on a small set determine the function throughout its domain.