Abstract
Given a set-valued map \(F:X\rightarrow \mathcal{P }(Z)\) from a topological space \(X\) to a metric space \((Z,d)\), we study distances from the set of selectors \({Sel}(F)\) to spaces of continuous functions and Baire one functions. For this we use some indexes related with the oscillation in single-valued maps that measure in some sense how far a set-valued map is from being upper or lower semicontinuous.
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I am grateful to the referees for their suggestions and corrections that have improved the paper.
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The research was supported the project MTM2011-25377 of the Spanish Ministry of Science and Innovation.
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Angosto, C. Distances from selectors to spaces of functions. RACSAM 108, 757–768 (2014). https://doi.org/10.1007/s13398-013-0138-2
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DOI: https://doi.org/10.1007/s13398-013-0138-2