Category
page 1Compactification (mathematics)
compactification
embedding a topological space into a compact space as a dense subset
Alexandroff extension
given a space X, the space X ⊔ {∞}, topologized so that a set containing ∞ is open iff its complement is closed compact in X
Stone–Čech compactification
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
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in topology, the connected components of the “ideal boundary” of a space