arXiv subjects
Publications and source records attributed to Narcisse Roland Loufouma Makala.
We prove a selection theorem for paraconvex-valued mappings defined on τ-PF normal spaces. The method developed to prove this result is used to provide a general approach to such selection theorems.
We prove that Michael's paraconvex-valued selection theorem for paracompact spaces remains true for C'(E)-valued mappings defined on collectionwise normal spaces. Some possible generalisations are also given.
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.