Normality-like properties, paraconvexity and selections.
dc.contributor.advisor | Gutev, V. | |
dc.contributor.author | Makala, Narcisse Roland Loufouma. | |
dc.date.accessioned | 2014-04-22T14:44:38Z | |
dc.date.available | 2014-04-22T14:44:38Z | |
dc.date.created | 2012 | |
dc.date.issued | 2012 | |
dc.description | Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2012. | en |
dc.description.abstract | In 1956, E. Michael proved his famous convex-valued selection theorems for l.s.c. mappings de ned on spaces with higher separation axioms (paracompact, collectionwise normal, normal and countably paracompact, normal, and perfectly normal), [39]. In 1959, he generalized the convex-valued selection theorem for mappings de ned on paracompact spaces by replacing \convexity" with \ -paraconvexity", for some xed constant 0 < 1 (see, [42]). In 1993, P.V. Semenov generalized this result by replacing with some continuous function f : (0;1) ! [0; 1) (functional paraconvexity) satisfying a certain property called (PS), [63]. In this thesis, we demonstrate that the classical Michael selection theorem for l.s.c. mappings with a collectionwise normal domain can be reduced only to compact-valued mappings modulo Dowker's extension theorem for such spaces. The idea used to achieve this reduction is also applied to get a simple direct proof of that selection theorem of Michael's. Some other possible applications are demonstrated as well. We also demonstrate that the -paraconvex-valued and the functionally-paraconvex valued selection theorems remain true for C 0 (Y )-valued mappings de ned on -collectionwise normal spaces, where is an in nite cardinal number. Finally, we prove that these theorems remain true for C (Y )-valued mappings de ned on -PF-normal spaces; and we provide a general approach to such selection theorems. | en |
dc.identifier.uri | http://hdl.handle.net/10413/10608 | |
dc.language.iso | en_ZA | en |
dc.subject | Selection theorems. | en |
dc.subject | Theses--Mathematics. | en |
dc.title | Normality-like properties, paraconvexity and selections. | en |
dc.type | Thesis | en |
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