?

Topology

Free Version

Upgrade subject to access all content

Easy

Riemann Sphere Approaching Infinity

TOPO-WENWKN

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

A

$0$

B

$1$

C

$\infty$

D

Does not exist.