Theorems of Namioka and R. E. Johnson type for upper semicontinuous and compact valued set-valued mappings-Reference-Cited by-同舟云学术

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

Published:1982 Issue:4 Volume:86 Page:649-655
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Christensen Jens Peter Reus

Abstract

Some recent results of Namioka on strong continuity of weakly continuous mappings (in a dense G δ {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1982-086-04/S0002-9939-1982-0674099-0/S0002-9939-1982-0674099-0.pdf

Reference5 articles.

1. Joint continuity of separately continuous functions;Christensen, Jens Peter Reus;Proc. Amer. Math. Soc.,1981

2. \bysame, 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. Separate continuity and measurability;Johnson, B. E.;Proc. Amer. Math. Soc.,1969

4. Dense strong continuity of pointwise continuous mappings;Kenderov, Petar;Pacific J. Math.,1980

5. Separate continuity and joint continuity;Namioka, I.;Pacific J. Math.,1974

Cited by 38 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Once again on topological spaces containing a dense completely metrizable subset;Topology and its Applications;2023-12

2. Minimal cusco maps and the topology of uniform convergence on compacta;Filomat;2023

3. Spaces of Minimal Usco and Minimal Cusco Maps as Fréchet Topological Vector Spaces;Advances in Topology and Their Interdisciplinary Applications;2023

4. Minimal usco maps and cardinal invariants of the topology of uniform convergence on compacta;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2021-10-23

5. When is the space of minimal usco/cusco maps a topological vector space;Journal of Mathematical Analysis and Applications;2020-09