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


Author: Jens Peter Reus Christensen
Journal: Proc. Amer. Math. Soc. 86 (1982), 649-655
MSC: Primary 54C60; Secondary 46B22, 46G99
DOI: https://doi.org/10.1090/S0002-9939-1982-0674099-0
MathSciNet review: 674099
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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 [Enhancements On Off] (What's this?)

  • [1] Jens Peter Reus Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), 455-461. MR 612739 (82h:54012)
  • [2] -, Remarks on Namioka spaces and R. E. Johnson's theorem on the norm separability of the range of certain mappings, Math. Scand. (to appear).
  • [3] R. E. Johnson, Separate continuity and measurability, Proc. Amer. Math. Soc. 82 (1969), 420-422. MR 0236345 (38:4641)
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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1982-0674099-0
Keywords: Automatic continuity in a dense $ {G_\delta }$ set, nonlinear automatic continuity, strong continuity of usco set-valued mappings
Article copyright: © Copyright 1982 American Mathematical Society

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