Definition:Uniform Convergence of Product/Compact Space

Definition
Let $X$ be a compact topological space.

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

Let $\left\langle{f_n}\right\rangle$ be a sequence of continuous mappings $f_n: X \to \mathbb K$.