Regular Sets, Scalar Multiplications and Abstractions of Distance Spaces

Abstract

<p> This thesis is both classically and abstractly oriented in a geometrical sense. The discussion is centred around the motion distance.</p> <p> In the first chapter, the concept of a regular set is defined and discussed. The idea of a regular set is a natural generalization of equilateral triangles and regular tetrahedra in Euclidean spaces.</p> <p> In chapter two, two kinds of scalar multiplication associated with metric spaces are studied.</p> <p> In chapter three, the concept of distance is abstracted to a level where it loses most of its structure. This abstraction is then examined.</p> <p> In chapter four, generalized metric spaces are examined. These are specializations of the abstract spaces of chapter three.</p>