Stone Cech Compactification

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Bol Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 ßX. The Stone-¿ech compactification ßX 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 ßX. If X is a Tychonoff space then the map from X to its image in ßX is a homeomorphism, so X can be thought of as a subspace of ßX. For general topological spaces X, the map from X to ßX need not be injective.

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 ßX. The Stone-¿ech compactification ßX 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 ßX. If X is a Tychonoff space then the map from X to its image in ßX is a homeomorphism, so X can be thought of as a subspace of ßX. For general topological spaces X, the map from X to ßX need not be injective.


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