Encyclopaedia of Mathematical Sciences

General Topology I

Basic Concepts and Constructions Dimension Theory

Editors: Arkhangel'skii, A.V., Pontryagin, L.S. (Eds.)

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About this 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.

Table of contents (2 chapter)

  • The Basic Concepts and Constructions of General Topology

    A. V. Arkhangel’skiǐ, V. V. Fedorchuk

    Pages 1-90

    Buy Chapter $29.95
  • The Fundamentals of Dimension Theory

    V. V. Fedorchuk

    Pages 91-192

    Buy Chapter $29.95
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Buy this book

eBook $99.00 net
( price for USA )
  • ISBN 978-3-642-61265-7
  • digitally watermarked, no DRM
  • included format: PDF
  • eBooks can be used on all Reading Devices
Softcover $129.00 net
( price for USA )
  • ISBN 978-3-642-64767-3
  • free shipping for individuals worldwide
  • usually dispatched within 3 to 5 business days

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Bibliographic Information

Bibliographic Information
Book Title
General Topology I
Book Subtitle
Basic Concepts and Constructions Dimension Theory
Series Title
Encyclopaedia of Mathematical Sciences
Series Volume
17
Copyright
1990
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-61265-7
DOI
10.1007/978-3-642-61265-7
Softcover ISBN
978-3-642-64767-3
Series ISSN
0938-0396
Edition Number
1
Topics