Content deleted Content added
→Proof: expanded on the use of Rouché's theorem and made some minor corrections |
clarified meaning of the smaller red circle |
||
Line 7:
==Proof==
[[Image:OpenMapping1.png|frame|right|Blue dots represent zeros of ''g''(''z''). Black spikes 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 circle is the
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'') is contained in a disk which is contained in ''f''(''U'').
| |||