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 ...
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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.
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Add this copy of Theorems and Problems in Functional Analysis (Problem to cart. $98.31, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 2011 by Springer.
Add this copy of Theorems and Problems in Functional Analysis to cart. $29.50, good condition, Sold by Second Story Books rated 5.0 out of 5 stars, ships from Rockville, MD, UNITED STATES, published 1982 by Springer-Verlag.
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Book. Octavo; G+/paperback; orange spine with maroon text; covers show slight shelf wear; some rubbing wear to joints; minor edge wear otherwise; intact binding; text block edges have modestly age toned; illustrated; pp 347. 1358164. FP New Rockville Stock.
Add this copy of Theorems and Problems in Functional Analysis (Problem to cart. $73.04, good condition, Sold by Stephen White Books rated 5.0 out of 5 stars, ships from Bradford, WEST YORKSHIRE, UNITED KINGDOM, published 1982 by Springer.
Add this copy of Theorems and Problems in Functional Analysis (Problem to cart. $119.50, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Newport Coast, CA, UNITED STATES, published 1982 by Springer.
Add this copy of Theorems and Problems in Functional Analysis to cart. $152.00, very good condition, Sold by Adkins Books rated 5.0 out of 5 stars, ships from Chattanooga, TN, UNITED STATES, published 1982 by Springer-Verlag Berlin and Heidelberg GmbH & Co. K.
Edition:
1982, Springer-Verlag Berlin and Heidelberg GmbH & Co. K
