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?