Compactification

Summary

A compactification of a topological space $X$ is a compact space that contains a copy of $X$ as a dense subspace. It adds "points at infinity" so that sequences or nets that escape $X$ get limits. Standard examples are the one-point compactification and the Stone–Čech compactification. A space has a Hausdorff compactification exactly when it is a Tychonoff space.