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- Open_mapping_theorem_(complex_analysis) abstract "In complex analysis, the open mapping theorem states that if U is a domain of the complex plane C and f : U → C is a non-constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of C).The open mapping theorem points to the sharp difference between holomorphy and real-differentiability. On the real line, for example, the differentiable function f(x) = x2 is not an open map, as the image of the open interval (−1, 1) is the half-open interval [0, 1). The theorem for example implies that a non-constant holomorphic function cannot map an open disk onto a portion of any real line embedded in the complex plane. Images of holomorphic functions can be of real dimension zero (if constant) or two (if non-constant) but never of dimension 1.".
- Open_mapping_theorem_(complex_analysis) thumbnail OpenMapping1.png?width=300.
- Open_mapping_theorem_(complex_analysis) wikiPageID "17395232".
- Open_mapping_theorem_(complex_analysis) wikiPageRevisionID "559550005".
- Open_mapping_theorem_(complex_analysis) hasPhotoCollection Open_mapping_theorem_(complex_analysis).
- Open_mapping_theorem_(complex_analysis) subject Category:Articles_containing_proofs.
- Open_mapping_theorem_(complex_analysis) subject Category:Theorems_in_complex_analysis.
- Open_mapping_theorem_(complex_analysis) type Abstraction100002137.
- Open_mapping_theorem_(complex_analysis) type Communication100033020.
- Open_mapping_theorem_(complex_analysis) type Message106598915.
- Open_mapping_theorem_(complex_analysis) type Proposition106750804.
- Open_mapping_theorem_(complex_analysis) type Statement106722453.
- Open_mapping_theorem_(complex_analysis) type Theorem106752293.
- Open_mapping_theorem_(complex_analysis) type TheoremsInComplexAnalysis.
- Open_mapping_theorem_(complex_analysis) comment "In complex analysis, the open mapping theorem states that if U is a domain of the complex plane C and f : U → C is a non-constant holomorphic function, then f is an open map (i.e. it sends open subsets of U to open subsets of C).The open mapping theorem points to the sharp difference between holomorphy and real-differentiability. On the real line, for example, the differentiable function f(x) = x2 is not an open map, as the image of the open interval (−1, 1) is the half-open interval [0, 1).".
- Open_mapping_theorem_(complex_analysis) label "Offenheitssatz".
- Open_mapping_theorem_(complex_analysis) label "Open mapping theorem (complex analysis)".
- Open_mapping_theorem_(complex_analysis) label "Teorema della funzione aperta (analisi complessa)".
- Open_mapping_theorem_(complex_analysis) label "Théorème de l'image ouverte".
- Open_mapping_theorem_(complex_analysis) label "Принцип сохранения области".
- Open_mapping_theorem_(complex_analysis) sameAs Offenheitssatz.
- Open_mapping_theorem_(complex_analysis) sameAs Théorème_de_l'image_ouverte.
- Open_mapping_theorem_(complex_analysis) sameAs Teorema_della_funzione_aperta_(analisi_complessa).
- Open_mapping_theorem_(complex_analysis) sameAs m.04g1zvz.
- Open_mapping_theorem_(complex_analysis) sameAs Q967972.
- Open_mapping_theorem_(complex_analysis) sameAs Q967972.
- Open_mapping_theorem_(complex_analysis) sameAs Open_mapping_theorem_(complex_analysis).
- Open_mapping_theorem_(complex_analysis) wasDerivedFrom Open_mapping_theorem_(complex_analysis)?oldid=559550005.
- Open_mapping_theorem_(complex_analysis) depiction OpenMapping1.png.
- Open_mapping_theorem_(complex_analysis) isPrimaryTopicOf Open_mapping_theorem_(complex_analysis).
