טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentWissam Boulos
SubjectBest Approximations; Farthest Points and Porosity
in Banach and Hyperbolic Spaces
DepartmentDepartment of Mathematics
Supervisor Professor Emeritus Reich Simeon
Full Thesis textFull thesis text - English Version


Abstract

This thesis presents several generic existence theorems and propositions concerning best approximations and farthest point problems in Banach and complete hyperbolic spaces using the notion of porosity.

In Chapter 1 of the thesis we define the notion of porosity and discuss a few of its properties.  Chapter 2 contains a survey of results for best approximation problems. In Chapter 3 we prove a farthest point theorem in complete hyperbolic spaces. Chapter 4 deals with a correction to the proof of a certain best approximation result in Banach spaces. In Chapter 5 we prove a best approximation result and a farthest point result in complete hyperbolic spaces. Chapter 6 gives a survey of theorems and propositions for farthest point problems in Banach spaces. In Chapter 7 we prove a geometry dependent farthest point theorem.