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## Degree of map

Algebraic Topology
Papapetros Vaggelis
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### Degree of map

Let $\displaystyle{p}$ be a polynomial function on $\displaystyle{\mathbb{C}}$ which has no root on $\displaystyle{S^{1}}$ .

Show that the number of roots of the equation $\displaystyle{p(z)=0\,,z\in\mathbb{C}}$ with $\displaystyle{|z|<1}$

is the degree of the map $\displaystyle{\bar{p}:S^{1}\longrightarrow S^{1}}$ specified by $\displaystyle{\bar{p}(z)=\dfrac{p(z)}{|p(z)|}}$ .