Explore: Hausdorff Compactifications

sense minimal among all compactifications; the disadvantage lies in the fact that it only gives a Hausdorff compactification on the class of locally compact

one-point compactification of X is Hausdorff if and only if X is Hausdorff and locally compact. Of particular interest are Hausdorff compactifications, i.e

has a Hausdorff compactification. Among those Hausdorff compactifications, there is a unique "most general" one, the Stone–Čech compactification β X .

compactification (or Čech–Stone compactification) is a technique for constructing a universal map from a topological space X to a compact Hausdorff space

general Hausdorff; All compact Hausdorff spaces are normal; In particular, the Stone–Čech compactification of a Tychonoff space is normal Hausdorff; Generalizing

convergence. This section explores compactifications of locally compact spaces. Every compact space is its own compactification. So to avoid trivialities it

In mathematics, the Bohr compactification of a topological group G is a compact Hausdorff topological group H that may be canonically associated to G.

other. Also some authors include some separation axiom (like Hausdorff space or weak Hausdorff space) in the definition of one or both terms, and others

one-point compactification. By the same construction, every locally compact Hausdorff space X is an open dense subspace of a compact Hausdorff space having

closure. The Stone–Čech remainder of a σ-compact and locally compact Hausdorff space is a sub-Stonean space, i.e., any two open σ-compact disjoint subsets