Let $\displaystyle n,m \geq 0$ be integers.

Suppose that for every $\displaystyle 0 \leq i \leq n$ and $\displaystyle 0 \leq i \leq m $ we have a real number $\displaystyle c_{ij}$.

Form the function $\displaystyle P:\mathbb{R}^2 \rightarrow \mathbb{R}^2$ defined by

$\displaystyle P(x,y) := \sum^n_{i=0}\sum^m_{j=0} c_{ij}x^iy^j$

I want to show that P is continuous. Any hints?