# Get An Introduction to Topology & Homotopy PDF By Allan J. Sieradski

ISBN-10: 0534929605

ISBN-13: 9780534929602

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Extra resources for An Introduction to Topology & Homotopy

Sample text

Let us suppose that, to the contrary, for any ( such that 0 < Zk = z~OY2nk, Izkl > 0, there exists a sequence of distinct numbers z k

Thi s extension Izl < 1 except at points that are mapped into and are poles of ¢ (z), and it maps the disk Izl < 1 onto a many-sheeted Riemann surface lying over the entire (­ plane. DO cluster points inside the disk Izl < 1 (see Figure 7). Let us suppose, to the is regular in contrary, that 00 Zo is a cluster point of the set of vertices of the grid and let Iz k }, contains infinitely many triangles of the modular grid and hence /l. (z) assumes in the subset of this neighborhood contained in and 00.

Has a subsequence that converges uniformly inside B to a regular function or to eian r 1 -I a II 00. This proves that the sequence la n 1 has no cluster 00. The situation is analogous with the remaining vertices of the domain B. Since each of the points z k is the image of a vertex of the triangle B under one of the functions z' no cluster points in 'zl < I, = 'ill "" I[(z) I of functions that are regular in a domain B is said to be normal in B if every sequence of functions belonging to that family 1-1 all = so that Ia n I -> 1 as n -- sults in turn lead to considerabl e further development of questions on the con­ by Montel, of a normal family of analytic functions (d.