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General Topology I

General Topology I


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About the Book

General topology is the domain ofmathematics devoted to the investigation of the concepts of continuity and passage to a limit at their natural level of generality. The most basic concepts of general topology, that of a topological space and a continuous map, were introduced by Hausdorffin 1914. Oneofthecentralproblemsoftopologyisthedeterminationandinvestigation of topological invariants; that is, properties ofspaces which are preserved under homeomorphisms. Topological invariants need not be numbers. Connectedness, compactness, andmetrizability, forexample, arenon-numericaltopologicalinvariants.Dimen- sional invariants, on the otherhand, areexamplesofnumericalinvariants which take integervalues on specific topological spaces. Part II ofthis book is devoted to them. Topological invariants which take values in the cardinal numbers play an especially important role, providing the raw material for many useful coin" putations. Weight, density, character, and Suslin number are invariants ofthis type. Certain classes of topological spaces are defined in terms of topological in- variants. Particularly important examples include the metrizable spaces, spaces with a countable base, compact spaces, Tikhonov spaces, Polish spaces, Cech- complete spaces and the symmetrizable spaces.


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Product Details
  • ISBN-13: 9783642647673
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Binding: Paperback
  • Height: 234 mm
  • No of Pages: 202
  • Series Title: Encyclopaedia of Mathematical Sciences
  • Sub Title: Basic Concepts and Constructions Dimension Theory
  • Width: 156 mm
  • ISBN-10: 3642647677
  • Publisher Date: 18 Sep 2011
  • Edition: Softcover reprint of the original 1st ed. 1990
  • Language: English
  • Returnable: N
  • Spine Width: 12 mm
  • Weight: 363 gr


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