Sequences of sets over a topological space define analogous convergence and boundness notions as sequences of vectors or numbers. Set convergence in the Painleve-Kuratowski sense provides a rigorous framework for the study of sequences of sets and the basis for the study of convergence properties of sequences of extended-real-valued functions and multi-valued mappings. In these notes we define the notions of inner and outer limits and we characterize them in the light of the underlying topology.
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