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Mar 12, 2011 at 16:35 comment added S. Carnahan I believe the correct claim is that the contour has winding number zero around the two distinguished points where the plane is punctured. Based on the picture, it certainly appears to have winding number 1 around any point in the lower right bounded region.
Mar 11, 2011 at 12:23 history answered Charles Matthews CC BY-SA 2.5