Note the similitude of this extension topology construction and the Alexandroff one-point compactification, in which case, having a topological space X which one wishes to compactify by adding a point ∞ in infinity, one considers the closed sets of X ∪ {∞} to be the sets of the form: K, where K is a closed compact set of X, or B ∪ {∞}, where B is a closed set of X.