By A. N. Kolmogorov, S. V. Fomin
Reprinted the following in a single quantity, the 1st half is dedicated to metric and general areas. starting with a short advent to set conception and mappings, the authors provide a transparent presentation of the speculation of metric and entire metric areas. the primary of contraction mappings and its purposes to the facts of life theorems within the concept of differential and indispensable equations gets targeted research, as do non-stop curves in metric areas — a subject matter seldom mentioned in textbooks.
Part One additionally contains discussions of different matters, equivalent to parts of the speculation of normed linear areas, susceptible sequential convergence of parts and linear functionals, adjoint operators, and linear operator equations. half makes a speciality of an exposition of degree concept, the Lebesque period and Hilbert house. either components characteristic a variety of workouts on the finish of every part and comprise important lists of symbols, definitions, and theorems.