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Home > Art, Film & Photography > Compactification: Stone- Ech Compactification, Alexandroff Extension, End, Bohr Compactification, Baily-Borel Compactification
Compactification: Stone- Ech Compactification, Alexandroff Extension, End, Bohr Compactification, Baily-Borel Compactification

Compactification: Stone- Ech Compactification, Alexandroff Extension, End, Bohr Compactification, Baily-Borel Compactification


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About the Book

Chapters: Stone- ech Compactification, Alexandroff Extension, End, Bohr Compactification, Baily-borel Compactification, Wallman Compactification. Source: Wikipedia. Pages: 33. Not illustrated. Free updates online. Purchase includes a free trial membership in the publisher's book club where you can select from more than a million books without charge. Excerpt: In the mathematical discipline of general topology, Stoneech compactification is a technique for constructing a universal map from a topological space X to a compact Hausdorff space X. The Stoneech 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 (in a unique way). 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 (dense) subspace of X. For general topological spaces X, the map from X to X need not be injective. A form of the axiom of choice is required to prove that every topological space has a Stoneech compactification. Even for quite simple spaces, an accessible concrete description of often remains elusive. In particular it is impossible to exhibit a point in explicitly. The Stoneech compactification was found by Marshall Stone (1937) and Eduard ech (1937). X is a compact Hausdorff space together with a continuous map from X and has the following universal property: any continuous map f: X K, where K is a compact Hausdorff space, lifts uniquely to a continuous map f: X K. As is usual for universal properties, this universal property, together with the fact that X is a compact Hausdorff space containing X, characterizes X up to homeomorphism. Some authors add the assumption that the starting space be Tychonoff (or even locally compact Hausdorff), for the following reasons: The Stoneech construction can be performed for more general spaces X, but the map X X need not be a ho...More: http: //booksllc.net/?id=52897


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Product Details
  • ISBN-13: 9781156175231
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Stone- Ech Compactification, Alexandroff Extension, End, Bohr Compactification, Baily-Borel Compactification
  • Width: 229 mm
  • ISBN-10: 1156175232
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 64 gr


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