ABSTRACT

This chapter presents textbooks and monographs that contain a detailed study of the structures. It explains the classical (multidimensional) analysis using functions defined on subsets of the Euclidean space, the major part of the discussion that follows deals with structures that are considerably richer than the one defined only by introduction of the topology. Nevertheless, such an object as a topological space and the corresponding general definition of continuity are very convenient initial concepts that are repeatedly used in the sequel. A metric space is automatically a Hausdorff space. A metric space differs from an arbitrary topological space by the possibility of introducing some additional concepts. The Abelian group enters into the definition of a linear space is used for defining a complex, namely, an algebraic equivalent of a geometric formation on which functions that are of interest to an analyst are defined.