 In fact, the converse is also true; being a Tychonoff space is both necessary and sufficient for possessing a Hausdorff compactification.The fact that large and interesting classes of non-compact spaces do in fact have compactifications of particular sorts makes compactification a common technique in topology.For any topological space "X" the (Alexandroff) one-point compactification α"X" of "X" is obtained by adding one extra point ∞ (often called a "point at infinity") and defining the open sets of the new space to be the open sets of "X" together with the sets of the form "G" ∪ {∞}, where "G" is an open subset of "X" such that "X" \ "G" is closed and compact.