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

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

and so on.