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Theorems and Problems in Functional Analysis by A. D. Gvishiani, A. A. Kirillov (Hardcover, 1982)

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Product Information

Even the simplest mathematical abstraction of the phenomena of reality the real line-can be regarded from different points of view by different mathematical disciplines. For example, the algebraic approach to the study of the real line involves describing its properties as a set to whose elements we can apply operations, and obtaining an algebraic model of it on the basis of these properties, without regard for the topological properties. On the other hand, we can focus on the topology of the real line and construct a formal model of it by singling out its continuity as a basis for the model. Analysis regards the line, and the functions on it, in the unity of the whole system of their algebraic and topological properties, with the fundamental deductions about them obtained by using the interplay between the algebraic and topological structures. The same picture is observed at higher stages of abstraction. Algebra studies linear spaces, groups, rings, modules, and so on. Topology studies structures of a different kind on arbitrary sets, structures that give mathe matical meaning to the concepts of a limit, continuity, a neighborhood, and so on. Functional analysis takes up topological linear spaces, topological groups, normed rings, modules of representations of topological groups in topological linear spaces, and so on. Thus, the basic object of study in functional analysis consists of objects equipped with compatible algebraic and topological structures.

Product Identifiers

Publisher
Springer-Verlag New York Inc.
ISBN-13
9780387906386
eBay Product ID (ePID)
178012739

Product Key Features

Author
A. D. Gvishiani, A. A. Kirillov
Publication Name
Theorems and Problems in Functional Analysis
Format
Hardcover
Language
English
Subject
Mathematics
Publication Year
1982
Type
Textbook
Number of Pages
347 Pages

Dimensions

Item Weight
730g

Additional Product Features

Title_Author
A. A. Kirillov, A. D. Gvishiani
Series Title
Problem Books in Mathematics
Country/Region of Manufacture
United States

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