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Home > Art, Film & Photography > Mathematical Comparisons: Comparison of Statistics Journals, Graphical Comparison of Musical Scales and Mathematical Progressions
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Mathematical Comparisons: Comparison of Statistics Journals, Graphical Comparison of Musical Scales and Mathematical Progressions

Mathematical Comparisons: Comparison of Statistics Journals, Graphical Comparison of Musical Scales and Mathematical Progressions


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About the Book

Chapters: Comparison of Statistics Journals, Graphical Comparison of Musical Scales and Mathematical Progressions, Comparison of Topologies, Comparison of General and Generalized Linear Models. 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 topology and related areas of mathematics comparison of topologies refers to the fact that two topological structures on a given set may stand in relation to each other. The set of all possible topologies on a given set forms a partially ordered set. This order relation can be used to compare the different topologies. Let ?1 and ?2 be two topologies on a set X such that ?1 is contained in ?2: .That is, every element of ?1 is also an element of ?2. Then the topology ?1 is said to be a coarser (weaker or smaller) topology than ?2, and ?2 is said to be a finer (stronger or larger) topology than ?1. If additionally we say ?1 is strictly coarser than ?2 and ?2 is strictly finer than ?1. The binary relation ? defines a partial ordering relation on the set of all possible topologies on X. The finest topology on X is the discrete topology. The coarsest topology on X is the trivial topology. In function spaces and spaces of measures there are often a number of possible topologies. See topologies on the set of operators on a Hilbert space for some intricate relationships. All possible polar topologies on a dual pair are finer than the weak topology and coarser than the strong topology. Let ?1 and ?2 be two topologies on a set X. Then the following statements are equivalent: Two immediate corollaries of this statement are One can also compare topologies using neighborhood bases. Let ?1 and ?2 be two topologies on a set X and let Bi(x) be a local base for the topology ?i at x ? X for i = 1,2. Then ?1 ? ?2 if and only if for all x...More: http: //booksllc.net/?id=1875382


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Product Details
  • ISBN-13: 9781156980071
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • No of Pages: 30
  • Spine Width: 2 mm
  • Weight: 59 gr
  • ISBN-10: 1156980070
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Sub Title: Comparison of Statistics Journals, Graphical Comparison of Musical Scales and Mathematical Progressions
  • Width: 229 mm


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