Generalized Virtually Stable Maps and Their Associated Sequences

Abstract EN

We extend the concept of virtual stability of continuous self-maps to arbitrary selfmaps and investigate the structure of sequences associated with uniformly virtually stable selfmaps.

We also obtain a necessary and sufficient condition for a uniformly virtually stable selfmap to have the largest possible associated sequence.

Examples of a uniformly virtually stable selfmap having the prescribed largest sequence and a uniformly virtually stable selfmap having no largest sequence are given.