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
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
Abstract: Some recent results of Namioka on strong continuity of weakly continuous mappings (in a dense 
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.
- [1] Jens Peter Reus Christensen, Joint continuity of separately continuous functions, Proc. Amer. Math. Soc. 82 (1981), no. 3, 455–461. MR 612739, https://doi.org/10.1090/S0002-9939-1981-0612739-1
- [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] B. E. Johnson, Separate continuity and measurability, Proc. Amer. Math. Soc. 20 (1969), 420–422. MR 0236345, https://doi.org/10.1090/S0002-9939-1969-0236345-0
- [4] Petar Kenderov, Dense strong continuity of pointwise continuous mappings, Pacific J. Math. 89 (1980), no. 1, 111–130. MR 596921
- [5] I. Namioka, Separate continuity and joint continuity, Pacific J. Math. 51 (1974), 515–531. MR 0370466
Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54C60, 46B22, 46G99
Retrieve articles in all journals with MSC: 54C60, 46B22, 46G99
Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1982-0674099-0
Keywords:
Automatic continuity in a dense 
set,
nonlinear automatic continuity,
strong continuity of usco set-valued mappings
Article copyright:
© Copyright 1982
American Mathematical Society