# Tychonoff Theorem

Let $(X,\tau)$ be a topological space, let $I$ be a set, and let $\left( \displaystyle\prod_{i \in I} X, \sigma \right)$ be a topological space where $\sigma$ is the product topology. If $\{K_i\}_{i \in I}$ is a collection of compact subsets of $X$, then the product $\displaystyle\prod C$ is a compact subset of $\displaystyle\prod_{i \in I} X$.