MathLearner123's latest activity

I have a question about Daniel Fischer's answer here Why the function ##g(w)## is well-defined on ##\mathbb{D} \setminus \{0\}##? I...

The below proposition is from David C. Ullrich's "Complex Made Simple" (pages 264-265) Proposition 14.5. Suppose ##D## is a bounded...

And note that, as you realize, the proof as given is incorrect, as it assumes V is connected; so the argument, and the choice of a fixed...

Oh so it will be a branch of logarithm in each connected, open part, and it will be something like a piecewise branch of logarithm on ##V##?

@WWGD if derivative of ##g## is constant, I still need to have that ##V## is domain to show that. So I also need that ##V## is connected.

I think that the statement is incorrect, and ##V## needs to be a domain (i.e. connected and open set), and this will make the statement...

I don't know if they are equal if ##V## is not connected.

I've read a proof from Complex Made Simple (David C. Ullrich) Proposition 4.3. Suppose that ##V## is an open subset of the plane. There...