 Formal completion commutes with restriction to an open subscheme

Restricting the topological structure sheaf of a formal completion of a scheme to an open subscheme commutes with its inverse limit: both sheaves are ${\underleftarrow{\lim }}_n({\mathcal{O}}_U/(\mathcal{I}{|}_U{)}^{n+1})$ on $|U\cap Y|$. Equivalently, the identical infinitesimal neighbourhoods have identical restricted structure sheaves. On formal affine charts this uses completed localization of an adic ring.

// Target: toric-geometry.bigb