General Topology I

Basic Concepts and Constructions Dimension Theory
Softcover Nachdruck of the original 1. Auflage 1990
ISBN: 978-3-642-64767-3
Verlag: Springer

Buch, Englisch, Band 17, 202 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 335 g

Reihe: Encyclopaedia of Mathematical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Arkhangel'skii, A. V.

Pontryagin, L. S.

Weitere Mitwirkende

O'Shea, D.B.

Arkhangel'skii, A.V.

Fedorchuk, V.V.

Inhaltsverzeichnis

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