Continuous Mappings
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Home > Art, Film & Photography > Continuous Mappings: Continuous Function, Uniform Continuity, Brouwer Fixed Point Theorem, Stone-Weierstrass Theorem
Continuous Mappings: Continuous Function, Uniform Continuity, Brouwer Fixed Point Theorem, Stone-Weierstrass Theorem

Continuous Mappings: Continuous Function, Uniform Continuity, Brouwer Fixed Point Theorem, Stone-Weierstrass Theorem


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About the Book

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 44. Chapters: Continuous function, Uniform continuity, Brouwer fixed point theorem, Stone-Weierstrass theorem, Intermediate value theorem, Tietze extension theorem, Borsuk-Ulam theorem, Absolute continuity, Arzela-Ascoli theorem, Space-filling curve, Homotopy, Equicontinuity, Minkowski's question mark function, Weierstrass function, Continuous wavelet transform, Bounded operator, Lefschetz fixed-point theorem, Degree of a continuous mapping, Open and closed maps, Maximum theorem, Continuous functions on a compact Hausdorff space, Hemicontinuity, Runge's phenomenon, Normal family, Proper map, Darboux's theorem, Bundle map, Blancmange curve, Banach-Stone theorem, Perfect map, Banach-Mazur theorem, Loop theorem, Triangular function, Direct image functor, Heine-Cantor theorem, Quillen adjunction, Michael selection theorem, Quasi-continuous function, Simplicial approximation theorem, Leray spectral sequence, Direct image with compact support, Continuous functional calculus, Symmetrically continuous function. Excerpt: Brouwer's fixed point theorem is a fixed point theorem in topology, named after Luitzen Brouwer. It states that for any continuous function f with certain properties there is a point x0 such that f(x0) = x0. The simplest form of Brouwer's theorem is for continuous functions f from a disk D to itself. A more general form is for continuous functions from a convex compact subset K of Euclidean space to itself. Among hundreds of fixed point theorems, Brouwer's is particularly well known, due in part to its use across numerous fields of mathematics. In its original field, this result is one of the key theorems characterizing the topology of Euclidean spaces, along with the Jordan curve theorem, the hairy ball theorem and the Borsuk-Ulam theorem. This gives it a place among the fundamental theorems of topology. The theorem is a...


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Product Details
  • ISBN-13: 9781157430025
  • Publisher: Books LLC, Wiki Series
  • Publisher Imprint: Books LLC, Wiki Series
  • Height: 246 mm
  • No of Pages: 46
  • Spine Width: 3 mm
  • Weight: 100 gr
  • ISBN-10: 1157430023
  • Publisher Date: 06 Jul 2011
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Continuous Function, Uniform Continuity, Brouwer Fixed Point Theorem, Stone-Weierstrass Theorem
  • Width: 189 mm


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