General Topology I

Basic Concepts and Constructions Dimension Theory
Mitarbeit: Arkhangel'skii, A.V.; Fedorchuk, V.V.; Übersetzung: O'Shea, D.B.; Herausgegeben von Arkhangel'skii, A.V.; Pontryagin, L.S.

• Broschiertes Buch

Produktbeschreibung

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 invariantsofthis 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.

Produktdetails

• Encyclopaedia of Mathematical Sciences .17
• Verlag: Springer / Springer Berlin Heidelberg / Springer, Berlin
• Artikelnr. des Verlages: 978-3-642-64767-3
• Softcover reprint of the original 1st ed. 1990
• Seitenzahl: 216
• Erscheinungstermin: 18. September 2011
• Englisch
• Abmessung: 235mm x 155mm x 12mm
• Gewicht: 334g
• ISBN-13: 9783642647673
• ISBN-10: 3642647677
• Artikelnr.: 36115257

Autorenporträt

First encyclopedia volume on topology, based on a highly successful Russian edition. The book is both nov- el enough to appeal to the professional mathematician and accessible enough for students to use as an introductory textbook.

Inhaltsangabe

I. The Basic Concepts and Constructions of General Topology.- II. The Fundamentals of Dimension Theory.- Author Index.