General Topology I

Basic Concepts and Constructions Dimension Theory

A.V. Arkhangel'skii, L.S. Pontryagin (Herausgeber)

Buch | Softcover

VII, 202 Seiten

2011 | 1. Softcover reprint of the original 1st ed. 1990
Springer Berlin (Verlag)
978-3-642-64767-3 (ISBN)

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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.

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.

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

Erscheint lt. Verlag	18.9.2011
Reihe/Serie	Encyclopaedia of Mathematical Sciences
Co-Autor	A.V. Arkhangel'skii, V.V. Fedorchuk
Übersetzer	D.B. O'Shea
Zusatzinfo	VII, 202 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	334 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	algebraic topology • Algebraische Topologie • Analysis • Funktionalnalysis • geometric topology • Geometrische Topologie • Topological Algebra • Topologische Algebra • Topology
ISBN-10	3-642-64767-7 / 3642647677
ISBN-13	978-3-642-64767-3 / 9783642647673
Zustand	Neuware