Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings
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- by Jens Peter Reus Christensen
- Proc. Amer. Math. Soc. 86 (1982), 649-655
- DOI: https://doi.org/10.1090/S0002-9939-1982-0674099-0
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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
- Jens Peter Reus Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), no.ย 3, 455โ461. MR 612739, DOI 10.1090/S0002-9939-1981-0612739-1 โ, Remarks on Namioka spaces and R. E. Johnsonโs theorem on the norm separability of the range of certain mappings, Math. Scand. (to appear).
- B. E. Johnson, Separate continuity and measurability, Proc. Amer. Math. Soc. 20 (1969), 420โ422. MR 236345, DOI 10.1090/S0002-9939-1969-0236345-0
- Petar Kenderov, Dense strong continuity of pointwise continuous mappings, Pacific J. Math. 89 (1980), no.ย 1, 111โ130. MR 596921
- I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515โ531. MR 370466
Bibliographic Information
- © Copyright 1982 American Mathematical Society
- 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