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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, and we have invariance of domain.).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 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 Openmappingtheorem.png?width=300.
- Open_mapping_theorem_(complex_analysis) wikiPageID "17395232".
- Open_mapping_theorem_(complex_analysis) wikiPageLength "4113".
- Open_mapping_theorem_(complex_analysis) wikiPageOutDegree "25".
- Open_mapping_theorem_(complex_analysis) wikiPageRevisionID "660978134".
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Category:Articles_containing_proofs.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Category:Theorems_in_complex_analysis.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Compact_set.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Compact_space.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Complex_analysis.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Complex_plane.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Continuous_function.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Domain_(mathematical_analysis).
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Extreme_value_theorem.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Holomorphic_function.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Identity_theorem.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Interior_(topology).
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Interior_point.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Interval_(mathematics).
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Invariance_of_domain.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Maximum_modulus_principle.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Onto.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Open_and_closed_maps.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Open_interval.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Open_map.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Open_mapping_theorem_(functional_analysis).
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Point_(geometry).
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Radius.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Real_line.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Root_of_a_function.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Rouchxc3xa9s_theorem.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Surjective_function.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink Zero_of_a_function.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLink File:Openmappingtheorem.png.
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLinkText "Open mapping theorem (complex analysis)".
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLinkText "Open mapping theorem".
- Open_mapping_theorem_(complex_analysis) wikiPageWikiLinkText "open mapping theorem".
- Open_mapping_theorem_(complex_analysis) hasPhotoCollection Open_mapping_theorem_(complex_analysis).
- Open_mapping_theorem_(complex_analysis) wikiPageUsesTemplate Template:Citation.
- 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) hypernym Domain.
- Open_mapping_theorem_(complex_analysis) type Protein.
- 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, and we have invariance of domain.).The open mapping theorem points to the sharp difference between holomorphy and real-differentiability.".
- Open_mapping_theorem_(complex_analysis) label "Open mapping theorem (complex analysis)".
- Open_mapping_theorem_(complex_analysis) sameAs Offenheitssatz.
- Open_mapping_theorem_(complex_analysis) sameAs Thxc3xa9orxc3xa8me_de_limage_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 Принцип_сохранения_области.
- Open_mapping_theorem_(complex_analysis) sameAs Açık_gönderim_teoremi_(karmaşık_analiz).
- Open_mapping_theorem_(complex_analysis) sameAs Q967972.
- Open_mapping_theorem_(complex_analysis) sameAs Q967972.
- Open_mapping_theorem_(complex_analysis) wasDerivedFrom Open_mapping_theorem_(complex_analysis)?oldid=660978134.
- Open_mapping_theorem_(complex_analysis) depiction Openmappingtheorem.png.
- Open_mapping_theorem_(complex_analysis) isPrimaryTopicOf Open_mapping_theorem_(complex_analysis).