General Topology I

Basic Concepts and Constructions Dimension Theory

A.V. Arkhangel'skii, D.B. O'Shea, A.V. Arkhangel'skii , L.S. Pontryagin

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English

Springer-Verlag Berlin and Heidelberg GmbH & Co. K
18 September 2011

Calculus & mathematical analysis; Geometry; Topology

Series: Encyclopaedia of Mathematical Sciences

Summary
Details

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.

Contributions by: A.V. Arkhangel'skii, V.V. Fedorchuk
Edited by: A.V. Arkhangel'skii, L.S. Pontryagin
Translated by: D.B. O'Shea
Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Country of Publication: Germany
Edition: Softcover reprint of the original 1st ed. 1990
Volume: 17
Dimensions: Height: 235mm, Width: 155mm, Spine: 11mm
Weight: 335g
ISBN: 9783642647673
ISBN 10: 3642647677
Series: Encyclopaedia of Mathematical Sciences
Pages: 216
Publication Date: 18 September 2011
Audience: College/higher education , Professional and scholarly , A / AS level , Further / Higher Education
Format: Paperback
Publisher's Status: Active