Mr Narcisse Roland Loufouma Makala

Narcisse Roland Loufouma Makala    Research topic: Continuous selections and geometry of metric spaces

Selections are an important tool for many mathematicians working not only in general topology, but also in functional analysis, multivalued analysis, approximation theory, convex geometry, control theory, mathematical economics, and several other areas. The axiom of choice guarantees the existence of a selection for any nonempty family of subsets of a given nonempty set. Note that the resulting selection is not necessarily continuous. The real challenge is finding a selection which satisfies an additional condition; that of continuity.

We study the existence of continuous selections for nonempty paraconvex-valued (including convex-valued) mappings.

We also study various connectedness properties in the setting of metric spaces, such as uniform Lipschitz-connectedness, local pathwise connectedness, and chainability, with the view of relating them to selection problem
Name:   Mr Narcisse Roland Loufouma Makala
     
Discipline:   Mathematics General Topology
Qualifications:   Post Grad Diploma
MSc
PhD
     
Emails:   Loufouma@ukzn.ac.za 
Supervisor:   Prof Dharmanand Baboolal

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