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We turn now to the set of tangent points on the graph.

This set must consist of isolated points and closed intervals.

The fact that there can not be any limit points of the set except in closed intervals follows from the argument used in Lemma 1, namely, that near any tangent point in the C-plane the curves C and Af are analytic, and therefore the difference between them must be a monotone function in some neighborhood on either side of the tangent point.

This prevents the occurrence of an infinite sequence of isolated tangent points.