# Sierpiński's Theorem

## Theorem

Let $\left({S, \tau}\right)$ be a compact connected Hausdorff space.

Let $\left\{{F_n: n \in \N}\right\}$ be a pairwise disjoint closed cover of $S$.

Then $F_n = S$ for some $n \in \N$.

## Proof

## Source of Name

This entry was named for Wacław Franciszek Sierpiński.