- #1

binbagsss

- 1,281

- 11

## Homework Statement

Hi,

As part of the proof that :

the set of periods ##\Omega_f ## of periods of a meromorphic ##f: U \to \hat{C} ##, ##U## an open set and ##\hat{C}=C \cup \infty ##, ##C## the complex plane, form a discrete set of ##C## when ##f## is a non-constant

a step taken in the proof (by contradiction) is :

there exists an ##w_{0} \in \Omega_{f} ## s.t for any open set ##U## containing ##w_{0}##, there is an ##w \in \Omega_{f} / {w_0} ## contained in ##U##

*Now the next step is the bit I am stuck on*By the standard trick in analysis, we can produce a sequence of periods ##\{w_n\}## such that ##w_{n} \neq w_{0} ## and ##\lim_{n\to \infty} w_{n} = w_0 ##

## Homework Equations

## The Attempt at a Solution

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It's been a few years since I've done analysis, and the 'trick' has no name so I am struggling to look it up and find it in google.

A proof of this to understand it's meaning is really what I'm after , what's the idea behind the construction / significance in the usual context it would arise

I am also confused with the notation, does ##n=0## ? So the sequence converges to it's first term, or is ##n## starting from one

Many thanks in advance