Free Version

Upgrade subject to access all content

Moderate

Nets and Mobius Transformations

TOPO-9N3Y6$

What is the limit of the net $f:\mathbb C\cup\{\infty\}\rightarrow\mathbb C\cup\{\infty\}$ sending $z\mapsto (z-1)/(z+1)$, where $\mathbb C\cup\{\infty\}$ as a directed set has the partial order given by comparing absolute values?

A

$0$

B

$1$

C

$\infty$

D

Does not exist.