A subgame property of stable equilibria

Stable sets project onto stable sets of subgames in the following sense: stable sets consist of normal form perfect equilibria; of any given ε, we could therefore look at the set of strategy profiles in a subgame that are induced by the set of ε-perfect equilibria in a neighbourhood of a stable set. Now take the limit, as ε goes to zero, of the closures of these sets. It is shown that the set so obtained contains a stable set of the subgame.