Consider in X ∪ P the topology whose open sets are of the form: A ∪ Q, where A is an open set of X and Q is a subset of P.Note that the closed sets of X ∪ P are of the form: B ∪ Q, where B is a closed set of X and Q is a subset of P.For these reasons this topology is called the extension topology of X plus P, with which one extends to X ∪ P the open and the closed sets of X.