Convergence of set-valued mappings: Equi-outer semicontinuity |
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Authors: | Adib Bagh and Roger J-B Wets |
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Affiliation: | (1) Department of Mathematics, University of California, 95616 Davis, CA, USA |
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Abstract: | The concept of equi-outer semicontinuity allows us to relate the pointwise and the graphical convergence of set-valued-mappings. One of the main results is a compactness criterion that extends the classical Arzelà-Ascolì theorem for continuous functions to this new setting; it also leads to the exploration of the notion of continuous convergence. Equi-lower semicontinuity of functions is related to the outer semicontinuity of epigraphical mappings. Finally, some examples involving set-valued mappings are re-examined in terms of the concepts introduced here.Research supported in part by a grant of the National Science Foundation. |
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Keywords: | 54C60 54B20 49J40 49J52 |
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