Basic concepts and constructions dimension theory
著者
書誌事項
Basic concepts and constructions dimension theory
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 17 . General topology / A.V. Arkhangelʹskiĭ,
Springer-Verlag, c1990
- : gw
- : us
- :pbk
- タイトル別名
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Obshchaya topologiya
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注記
Translation of: "Obshchai︠a︡ topologii︠a︡ I," which is vol. 17 of the serial "Itogi nauki i tekhniki. Serii︠a︡ Sovremennye problemy matematiki. Fundamentalʹnye napravlenii︠a︡."
Includes bibliographical references and indexes
内容説明・目次
- 巻冊次
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: gw ISBN 9783540181781
内容説明
This is the first of the encyclopaedia volumes devoted to general topology. It has two parts. The first outlines the basic concepts and constructions of general topology, including several topics which have not previously been covered in English language texts. The second part presents a survey of dimension theory, from the very beginnings to the most important recent developments. The principal ideas and methods are treated in detail, and the main results are provided with sketches of proofs. The authors have produced a book which will not only be accessible to the general scientist and the undergraduate, but will also appeal to the professional mathematician. The authors' efforts to detail the relationship between more specialized topics and the central themes of topology give the book a broad scholarly appeal which transcends narrow disciplinary lines.
目次
I. The Basic Concepts and Constructions of General Topology.- II. The Fundamentals of Dimension Theory.- Author Index.
- 巻冊次
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:pbk ISBN 9783642647673
内容説明
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.
目次
I. The Basic Concepts and Constructions of General Topology.- II. The Fundamentals of Dimension Theory.- Author Index.
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