Open mapping theorem (complex analysis): Difference between revisions

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Revision as of 01:39, 31 October 2008

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The theorem for example implies that a non-constant [[holomorphic function]] cannot map an open disk ''[[onto]]'' a portion of a line.

=== 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 set ''B'' constructed in the proof.]]