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High Quality Content by WIKIPEDIA articles! In the mathematical discipline of general topology, Stone ech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space X. The Stone ech compactification X of a topological space X is the largest compact Hausdorff space "generated" by X, in the sense that any map from X to a compact Hausdorff space factors through X. If X is a Tychonoff space then the map from X to its image in X is a homeomorphism, so X can be thought of as a subspace of X. For general topological spaces X, the map from X to X need not be injective.