Sharing on a punctured domain and normality

Let \(D \subset {\mathbb {C}}\) $D\subset \mathbb{C}$ be a domain and \(D'=D {\setminus }\{z_0\}\) $D^{\prime }=D\backslash \{z_0\}$ , \(z_0 \in D\) $z_0\in D$ . By considering the sharing of a set of meromorphic functions by the members of a family \({\mathcal {F}}\) $\mathcal{F}$ of holomorphic functions on \(D'\) $D^{\prime }$ , we prove the members of \({\mathcal {F}}\) $\mathcal{F}$ can be extended to be meromorphic on D, and the extended family \(\widehat{{\mathcal {F}}}\) $\widehat{\mathcal{F}}$ is normal in D.