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Author: Ipate Dumitru Degree: doctor habilitat of physics and mathematics Speciality:  01.01.04 - Geometry and topology Year: 2007 Scientific consultant: Mitrofan Cioban doctor habilitat, professor Institution: Scientific council:

Status The thesis was presented on the 15 November, 2007 Approved by NCAA on the 20 December, 2007 Abstract – 0.49 Mb / in romanian Thesis CZU 513.83 1.23 Mb / in romanian 184 pages

Keywords

Summary

The thesis is devoted to general theory of set-valued mappings and their applications.

The following problems are considered în the thesis:

• the approximation of set-valued mappings with the special mappings;
• the operations on set-valued mappings;
• the construction of subspaces of functional spaces with the special problems

For this aim, on the spaces of subsets we study the semi-continuous topologies, the exponential topology and the Hausdorff topology.These facts permit us:

• to consider different classes of continues mappings;
• to solve distinct approximation problems of the Chebyshev-Weierstrass type;
• the approximation of mappings în the spaces with Nachbin weight and the spaces with weights with sensible sign;
• to construct the dense subspaces of functional spaces.

The results of thesis have solved some problems raised by other mathematicians and can be applied for further investigations în the theory of mappings and functions, în the theory of topological spaces and in the courses of lectures.

Oficial Reviewers

• Dumitru Botnaru
  doctor habilitat, professor, Tiraspol State University
• Bogatyi Semion
  doctor habilitat în stiinţe fizico-matematice, profesor universitar, Universitatea de Stat «M.V. Lomonosov» din Moscova, Russia
• Nedev Stoian
  doctor habilitat în stiinţe fizico-matematice, profesor universitar, Institutul de Matematică şi Informatică al Academiei de Ştiinţe a Bulgariei, Sofia, Bulgaria

 Theses