Open mapping theorem
that map a half plane to the unit disk. And, thanks to Ullrich’s book, I know that there is a way to do this which is really cool and impossible to forget. Let U be the upper half plane and D be the open unit disk. The neat geometric observation is that 1Why? Because the correct de nition of connectedness excludes the empty space. Otherwise we
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www.uio.noabstract and di cult to fully comprehend than the subsequent de nition on a continuous map. The situation is analogous to that in linear algebra, where we say that a function f: V !W between real vector spaces is linear if it satis es f( x+ y) = f(x) + f(y)