Title: Theory / Important / Math / Analysis / Complex

Smaller0: \(\lim_{\Omega\ni x\to \xi}f\) exists and is distinct from \(f(\xi)\)
Greater0: there exists \(g:E\to\mathbb R\) continuous, such that \(f=g\) on \(\Omega\subseteq\{\xi\}\)
Page: https://en.wikipedia.org/wiki/Removable_singularity
Chapter: 4
Section: i
Variables: \(\omega\subseteq\mathbb C\) a region
\(f:\omega\setminus\{\xi\}\to\mathbb C\)
Assuming: f is holomorphic
Intermediate: \(\lim_{z\to\xi}(z-\xi)f(z)=0\)
Equivalent: there exists \(g:E\to\mathbb R\) holomorphic, such that \(f=g\) on \(\Omega\setminus\{\xi\}\)