Some recent results of Namioka on strong continuity of weakly continuous mappings (in a dense G δ {G_δ } set) and results of R. E. Johnson on norm separability of the range of such mappings (under conditions on the domain space) are shown to have analogues for upper semicontinuous and compact valued set-valued mappings. Some substantial improvements of known automatic continuity results for such mappings are obtained.
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Jens Peter Christensen (1982) studied this question.