A convention.

Before proceeding further, we employ the following convention.

For an open covering $\{U_\lambda\}_{\lambda \in \Lambda}$ of a topological space $X$ , we write

$$U_{\lambda \mu}=U_\lambda \cap U_\mu ,\qquad U_{\lambda \mu \nu}=U_\lambda \cap U_\mu \cap U_\nu,$$

and so on.