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In my textbook the following theorem is designated "Proposition 3.4.2 part (vi)". There are 6 parts total in the overall theorem. I'll just type the part I'm interested in below. My question is, is there a more standard name for this theorem? I would like to find an additional introduction to it if possible.

Let ##f## be meromorphic on the open connected set ##\Omega\subseteq \hat{\mathbb{C}}## and let ##A## be the set of its poles in ##\Omega##. Then:

(a) ##A## is a countable set.

(b) The accumulation points of ##A## are on the boundary of ##\Omega##.

(c) The set ##\Omega \setminus A## is open.

(d) If ##K## is a compact subset of ##\Omega##, then ##A\cap K## is a finite set.

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# Complex Analysis: Theorem Name

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