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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Vector & tensor analysis
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Theorems and Problems in Functional Analysis (Hardcover, 1982 ed.)
Loot Price: R2,476
Discovery Miles 24 760
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Theorems and Problems in Functional Analysis (Hardcover, 1982 ed.)
Series: Problem Books in Mathematics
Expected to ship within 18 - 22 working days
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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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