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https://knowledgecommons.lakeheadu.ca/handle/2453/2251
Title: | Linearization of an abstract convexity space |
Authors: | Yong, Sin |
Keywords: | Convex sets |
Issue Date: | 1978 |
Abstract: | Axiomatic convexity space, introduced by Kay and Womble [22] , will be the main topic discussed in this thesis. An axiomatic convexity space (X,C), which is domain finite and has regular straight segments, is called a basic convexity space, A weak complete basic convexity space is a basic convexity space which is complete and has C-isomorphic property. If in addition, it is join-hull commutative then it is called (strong) complete basic convexity space. The main results presented are: a generalized line space is a weak complete basic convexity space, a complete basic convexity space is equivalent to a line space; and a complete basic convexity space whose dimension is greater than two or desarguesian and of dimension two, is a linearly open convex subset of a real affine space. Finally, we develop a linearization theory by following an approach given by Bennett [3]. A basic convexity space whose dimension is greater than two, which is join-hull commutative and has a parallelism property, is an affine space. It can be made into a vector space over an ordered division ring and the members of C are precisely the convex subsets of the vector space. |
URI: | http://knowledgecommons.lakeheadu.ca/handle/2453/2251 |
metadata.etd.degree.discipline: | Mathematical Sciences |
metadata.etd.degree.name: | Master of Science |
metadata.etd.degree.level: | Master |
metadata.dc.contributor.advisor: | Whitfield, John |
Appears in Collections: | Retrospective theses |
Files in This Item:
File | Description | Size | Format | |
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YongS1978m-1b.pdf | 5.59 MB | Adobe PDF | ![]() View/Open |
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