The place of the theory of functions of a real variable among the mathematical disciplines
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Examining the monographs and textbooks on the theory of functions, one may notice that, as a rule, they do not give any comparatively brief definition of the subject matter of this mathematical discipline, as is done, for example, for topology—the study of the properties of topological spaces that are invariant under homeomorphisms—or algebra—the study of operations on elements of sets of arbitrary nature. The definition of the theory of functions occasionally encountered, as the study of the general properties of functions, is essentially a tautology.
KeywordsClassical Analysis Real Variable Trigonometric Series Functional Continuum Mathematical Discipline
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