Let $X$ be a paracompact Hausdorff [topological space](/page/Topological%20Space) and let $\mathcal U=\{U_i\}_{i\in I}$ be a finite family of open subsets of $X$ such that \begin{align*} X=\bigcup_{i\in I}U_i. \end{align*} Suppose that for every nonempty finite subset $\sigma\subset I$, the intersection \begin{align*} \bigcap_{i\in\sigma}U_i \end{align*} is either empty or contractible. Then $X$ is homotopy equivalent to $|N(\mathcal U)|$.