ABSTRACT
In the preceding chapter, each class of structured sets was considered on its own, without being associated with other structures. In practice, as a rule, one has to deal with mixed structures, i.e. with sets that are endowed with different types of structures simultaneously. Now we consider objects with a mixed structure, i.e. composites. It turns out that when these structures are in some sense consistent with each other, the sets acquire some additional, sometimes very rich properties, which are not characteristic for "clean" structures. We confine ourselves to considering sets endowed with both an algebraic and topological structures. The discussed problems corresponds to the foundations of functional analysis, which is a natural generalization of classical mathematical analysis to infinite-dimensional objects. The considered problems have important applications in the theory of differential equations and mathematical physics, optimal control theory and computational mathematics, probability theory and game theory.
