The closure and union operations on a set of simplices in a simplicial complex commute

Suppose K is a simplicial complex, and Λ = {S _α} _α its subset. Let T be the union of {S _α} _α and U the union of {Int S _α} _α. Clearly T is contained in the closure of U. But the other inclusion is also true; suppose x is a point in |K| not in T. Then it is in the interior of a simplex not in Λ, hence x is not in the closure of U.