Compactification (mathematics)

embedding a topological space into a compact space as a dense subset

given a space X, the space X ⊔ {∞}, topologized so that a set containing ∞ is open iff its complement is closed compact in X

a universal map from a topological space X to a compact Hausdorff space βX, such that any map from X to a compact Hausdorff space factors through βX uniquely; if X is Tychonoff, then X is a dense subspace of βX

in topology, the connected components of the “ideal boundary” of a space