O'Reilly logo

Dynamics in One Complex Variable. (AM-160), 3rd Edition by John Milnor

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

§17. Prime Ends and Local Connectivity

Carathéodory’s theory of “prime ends” is the basic tool for relating an open set of complex numbers to its complementary closed set. Let U be a simply connected subset of image such that the complement image \ U is infinite. The Riemann Mapping Theorem asserts that there exists a conformal isomorphism

image

In some cases, ψ will extend to a homeomorphism from the closed disk onto the closure , so that the topological boundary ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required