## Continuous

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

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

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

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

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