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http://hdl.handle.net/11375/17677
Title: | Regular Sets, Scalar Multiplications and Abstractions of Distance Spaces |
Authors: | Drake, James Stanley |
Advisor: | Lane, N.D. |
Department: | Mathematics |
Keywords: | motion distance, regular set, Euclidean spaces, abstracted, metric |
Publication Date: | May-1971 |
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> |
URI: | http://hdl.handle.net/11375/17677 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Drake_James_S._1971May_Ph.D..pdf | 7.54 MB | Adobe PDF | View/Open |
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