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Home > Art, Film & Photography > Separation Axioms: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space
Separation Axioms: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space

Separation Axioms: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space


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About the Book

Chapters: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space, Regular Space, T1 Space, Topological Indistinguishability, History of the Separation Axioms, Completely Hausdorff Space, Monotonically Normal Space, Sober Space, Dowker Space, Collectionwise Normal, Semiregular Space. Source: Wikipedia. Pages: 79. 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 fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff. The separation axioms are axioms only in the sense that, when defining the notion of topological space, you could add these conditions as extra axioms to get a more restricted notion of what a topological space is. The modern approach is to fix once and for all the axiomatization of topological space and then speak of kinds of topological spaces. However, the term "separation axiom" has stuck. The separation axioms are denoted with the letter "T" after the German "Trennungsaxiom," which means separation axiom. The precise meanings of the terms associated with the separation axioms has varied over time, as explained in History of the separation axioms. Especially when reading older literature, be sure to get the authors' definition of each condition mentioned to make sure that you know exactly what they mean. Before we define the separation axioms themselves, we give concrete meaning to the concept of separated sets (and points) in topological spaces. (But separated sets are not the same as separated spaces, defined in the next section.) The separation axioms are about the ...More: http: //booksllc.net/?id=5289


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Product Details
  • ISBN-13: 9781155682488
  • Publisher: Books LLC
  • Publisher Imprint: Books LLC
  • Height: 152 mm
  • Sub Title: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space
  • Width: 229 mm
  • ISBN-10: 1155682483
  • Publisher Date: 15 Sep 2010
  • Binding: Paperback
  • Spine Width: 5 mm
  • Weight: 127 gr


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Separation Axioms: Hausdorff Space, Separation Axiom, Paracompact Space, Normal Space, Tychonoff Space, Urysohn's Lemma, Kolmogorov Space
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