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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 uniformlyvirtually stable selfmap to have the largest possible associated sequence. Examples of a uniformly virtually stable selfmap havingthe prescribed largest sequence and a uniformly virtually stableselfmap having no largest sequence are given

Generalized Virtually Stable Maps and Their Associated Sequences