Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings

Christensen, Jens Peter Reus

doi:10.1090/S0002-9939-1982-0674099-0

Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings
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Proc. Amer. Math. Soc. 86 (1982), 649-655 Request permission

Abstract:

Some recent results of Namioka on strong continuity of weakly continuous mappings (in a dense ${G_\delta }$ 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.

References

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Remarks on Namioka spaces and R. E. Johnson’s theorem on the norm separability of the range of certain mappings

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