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Home > Art, Film & Photography > Uniform Spaces Uniform Spaces: Uniform Space, Totally Bounded Space, Uniformizable Space, Uuniform Space, Totally Bounded Space, Uniformizable Space, Uniform Property, Uniform Iso
Uniform Spaces Uniform Spaces: Uniform Space, Totally Bounded Space, Uniformizable Space, Uuniform Space, Totally Bounded Space, Uniformizable Space, Uniform Property, Uniform Iso

Uniform Spaces Uniform Spaces: Uniform Space, Totally Bounded Space, Uniformizable Space, Uuniform Space, Totally Bounded Space, Uniformizable Space, Uniform Property, Uniform Iso


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About the Book

PMChapters: Uniform Space, Totally Bounded Space, Uniformizable Space, Uniform Property, Uniform Isomorphism, Uniformly Connected Space. Source: Wikipedia. Pages: 29. 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 field of topology, a uniform space is a set with a uniform structure. Uniform spaces are topological spaces with additional structure which is used to define uniform properties such as completeness, uniform continuity and uniform convergence. The conceptual difference between uniform and topological structures is that in a uniform space, one can formalize certain notions of relative closeness and closeness of points. In other words, ideas like "x is closer to a than y is to b" make sense in uniform spaces. By comparison, in a general topological space, given sets A,B it is meaningful to say that a point x is arbitrarily close to A (i.e., in the closure of A), or perhaps that A is a smaller neighborhood of x than B, but notions of closeness of points and relative closeness are not described well by topological structure alone. Uniform spaces generalize metric spaces and topological groups and therefore underlie most of analysis. There are three equivalent definitions for a uniform structure. A uniform space (X, ) is a set X equipped with a nonempty family of subsets of the Cartesian product X x X ( is called the uniform structure or uniformity of X and its elements entourages (French: neighborhoods or surroundings)) that satisfy the following axioms: If the last property is omitted we call the space quasiuniform. One usually writes U={y : (x,y)U}. On a graph, a typical entourage is drawn as a blob surrounding the "y=x" diagonal; the Us are then the vertical cross-sections. If (x,y) U, one says that x and y are U-close. Similarly, if all pairs of points in a subse...More: http://booksllc.net/?id=323


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Product Details
  • ISBN-13: 9781157047070
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Uniform Space, Totally Bounded Space, Uniformizable Space, Uuniform Space, Totally Bounded Space, Uniformizable Space, Uniform Property, Uniform Iso
  • Width: 229 mm
  • ISBN-10: 1157047076
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 2 mm
  • Weight: 59 gr


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