Definition:Uniform Convergence of Product/Compact Space

Definition
Let $X$ be a set.

Let $\mathbb K$ be a field with absolute value $\left\vert{\cdot}\right\vert$.

Let $(f_n)$ be a sequence of mappings $f_n:X\to \mathbb K$.

The infinite product $\displaystyle \prod_{n \mathop = 1}^\infty f_n$ converges uniformly if the sequence of partial products converges uniformly.

Also see

 * Definition:Uniform Absolute Convergence of Product