Electronic Theses and Dissertations

Award/Availability

Open Access Thesis

Keywords

Minkowski geometry; Generalized spaces;

Abstract

In this work we investigate the behavior of the Minkowski Functionals admitted by a sequence of sets which converge to the unit ball ‘from the inside’. We begin in R 2 and use this example to build intuition as we extend to the more general R n case. We prove, in the penultimate chapter, that convergence ‘from the inside’ in this setting is equivalent to two other characterizations of the convergence: a geometric characterization which has to do with the sizes of the faces of each polytope in the sequence converging to zero, and the convergence of the Minkowski functionals defined on the approximating sets to the Euclidean Norm. In the last chapter we explore how we can extend our results to infinite dimensional vector spaces by changing our definition of polytope in that setting, the outlook is bleak.

Date of Award

2016

Degree Name

Master of Arts

Department

Department of Mathematics

First Advisor

Douglas Musapiri, Chair

Date Original

5-2016

Object Description

1 PDF file (vii, 28 pages)

Language

EN

File Format

application/pdf

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