On the structure of transitive \(\omega\)-limit sets for continuous maps
The goal of this paper is to discuss the admissible topological structure of \(\omega\)-limit sets for continuous maps on compact metric spaces. The author considers the problem from continuum theory point of view and describes the admissible topological structure of \(\omega\)-limit sets using the notion of arc component of a set. It is proved that for a complete characterization of \(\omega\)-limit sets in terms of arc components, one should take into account not only the number of arc components and their intersections but also the way in which convergence continua in the set are approximated.
scientific article; zbMATH DE number 2071091
scientific article