KnowraStone–Čech compactificationLinked fromLinked fromThe 11 pages that link to Stone–Čech compactification, each with the reason it gives.All 11Broader topic 4Related 7Compact spaceBroader topic: It embeds a space densely into a compact space to apply compact-space methods.Universal propertyBroader topic: Its extension property uniquely extends continuous maps into compact Hausdorff spaces.Hausdorff spaceBroader topic: Its defining target combines compactness with Hausdorff separation.Tychonoff's theoremRelated: Product compactness supports constructions of this universal compactification.UltrafilterRelated: For a discrete set, its points can be identified with ultrafilters on that set.Normal spaceRelated: Normal spaces are completely regular when they are also Hausdorff, linking them to this construction.Riesz–Markov–Kakutani representation theoremRelated: It connects bounded continuous functions on a noncompact space to continuous functions on a compact space.Separation axiomRelated: Complete regularity determines when this universal compactification is available.Urysohn's lemmaRelated: Urysohn functions help construct the continuous maps used to characterize this compactification.Adjoint functorsBroader topic: Its universal property presents compactification as a reflection, hence an adjunction.Stone's representation theorem for Boolean algebrasRelated: For a discrete set, its Stone–Čech compactification is the Stone space of its power-set algebra.