DearMHFmembers, here is my problem.

Suppose that we are given a real- or complex-valued function $\displaystyle f$

on a rectangular domain $\displaystyle D:=[a,b]\times[c,d]\subset\mathbb{R}^{2}$ such that

$\displaystyle f(t,\cdot)$ is continuous on $\displaystyle [c,d]$ for each fixed $\displaystyle t\in[a,b]$, and

$\displaystyle f(\cdot,s)$ is continuous on $\displaystyle [a,b]$ for each fixed $\displaystyle s\in[c,d]$.

- Does this mean that $\displaystyle f$ is continuous on $\displaystyle D$?
- If not, give a counter example, and provide additional

conditions on $\displaystyle f$ so that it continuous on $\displaystyle D$?

Thank you very much.

bkarpuz