Overview
- Authors:
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A. A. Kirillov
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Mathemathics Department, Moscow State University, Moscow, USSR
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A. A. Gvishiani
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Applied Mathemathics Laboratory, Institute of Earth Physics of the Academy of Sciences of the USSR, Moscow, USSR
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Table of contents (15 chapters)
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Theory
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- A. A. Kirillov, A. A. Gvishiani
Pages 3-11
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- A. A. Kirillov, A. A. Gvishiani
Pages 12-37
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- A. A. Kirillov, A. A. Gvishiani
Pages 38-94
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- A. A. Kirillov, A. A. Gvishiani
Pages 95-115
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- A. A. Kirillov, A. A. Gvishiani
Pages 116-135
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Problems
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Front Matter
Pages 137-137
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- A. A. Kirillov, A. A. Gvishiani
Pages 139-149
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- A. A. Kirillov, A. A. Gvishiani
Pages 150-169
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- A. A. Kirillov, A. A. Gvishiani
Pages 170-203
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- A. A. Kirillov, A. A. Gvishiani
Pages 204-218
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- A. A. Kirillov, A. A. Gvishiani
Pages 219-230
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Hints
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Front Matter
Pages 231-231
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- A. A. Kirillov, A. A. Gvishiani
Pages 233-243
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- A. A. Kirillov, A. A. Gvishiani
Pages 244-270
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- A. A. Kirillov, A. A. Gvishiani
Pages 271-308
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- A. A. Kirillov, A. A. Gvishiani
Pages 309-324
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- A. A. Kirillov, A. A. Gvishiani
Pages 325-334
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Back Matter
Pages 335-347
About this book
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.
Authors and Affiliations
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Mathemathics Department, Moscow State University, Moscow, USSR
A. A. Kirillov
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Applied Mathemathics Laboratory, Institute of Earth Physics of the Academy of Sciences of the USSR, Moscow, USSR
A. A. Gvishiani