### Book chapter

## О свойствах модулярных пространств

We present basic concepts of the theory of modular spaces on arbitrary sets, which

extends simultaneously the theory of such spaces on linear sets and the theory of

metric spaces. We study the relationship between (three) modular spaces and metrics

on them in the convex and nonconvex cases. We define the modular notions of

convergence, topology and completeness. We exhibit transformations of modular

spaces (for the right inverse modular), connected with their duality. The assertions

are illustrated by examples.