Revision as of 06:21, 11 June 2017 edit 216.252.90.94 (talk) →Applications: The L was capital, thus not linking to the existent wiki page. ← Previous edit		Revision as of 16:05, 22 March 2021 edit undo Belbury (talk \| contribs) Extended confirmed users, Rollbackers 84,347 edits →Proof: image is too large Next edit →
Line 7: ==Proof== [[Image:Openmappingtheorem.png\|thumb\|right\|~~500px~~upright=1.4\| Black dots represent zeros of ''g''(''z''). Black annuli represent poles. The boundary of the open set ''U'' is given by the dashed line. Note that all poles are exterior to the open set. The smaller red disk is ''B'', centered at ''z''<sub>0</sub>.]] Assume ''f'' : ''U'' → '''C''' is a non-constant holomorphic function and ''U'' is a [[Domain (mathematical analysis)\|___domain]] of the complex plane. We have to show that every [[Point (geometry)\|point]] in ''f''(''U'') is an [[interior point]] of ''f''(''U''), i.e. that every point in ''f''(''U'') has a neighborhood (open disk) which is also in ''f''(''U'').

Open mapping theorem (complex analysis): Difference between revisions