Null homologous

Description

A loop is called null homologous in $U$ if its Winding number is zero for all points outside of $U$. This generalised the idea of a Nullhomotopie.

Definition

Sei $U\subseteq \mathbb{C}$ Eine Stückweise Differenzierbare Schleife $\gamma$ heißt nullhomolog in $U$, wenn das Innere einer Schleife von $\gamma$ in $U$ enthalten ist: $\{z\in \mathbb{C}\backslash Spur(\gamma ):n(\gamma ,z)\ne 0\}\subseteq U$