# Tagged Questions

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### How to write the condition for Image of a function?

If $\Omega_l$ is $\Omega$ with $|x|<l$ and if $\Omega_S$ is the image of $z$ under mapping how we will write the condition for it. Am I right if I write $\Omega_S$ is $\Omega$ with $|S|<l$ or ...
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### Is there a name for the one-point compactification of $\mathbb{C}$?

Let $\hat{\mathbb{C}}$ be the one-point compactification of $\mathbb{C}$. This space $\hat{\mathbb{C}}$ is called the Riemann sphere. If I want to designate the topology $\tau$ on ...
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### What is this metric called?

Ahlfors -complex analysis p.20 Consider a stereographic projection between the 2-sphere and $\overline{\mathbb{C}}$ (i.e. one-point compactification of $\mathbb{C}$) Let $z,w$ be complex numbers. ...
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### If $\zeta$ is a function of characters what does it mean for it to be regular?

This is from lemma 2.4.1 of Tate's thesis. Lemma 2.4.1: A $\zeta$-function is regular in the "domain" of all quasi-characters of exponent greater than $0$. proof: We must show that for each ...
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### How do i visualize plots illustrating complex functions?

Here's an example : http://en.m.wikipedia.org/wiki/Essential_singularity What is this colored diagram illustrating complex function called? And how should i understand this diagram? What do colors ...