A survey of modern dimension theory

Halfyard, Clayton Walter (1971) A survey of modern dimension theory. Masters thesis, Memorial University of Newfoundland.

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    Available under License - The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
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Abstract

The main objective of this thesis is to give an up-to-date account of several dimension functions and relations that exist between them for various spaces. -- Chapter 1 contains a brief history of the development of the subject as we know it today. In Chapter 2 we give definitions of the three basic dimension functions 'ind', 'dim', and 'Ind' and a detailed survey of the known properties of these functions. Included is a proof of the famous Čech Sum Theorem for dimension 'dim'. -- In Chapter 3 we investigate relations between 'ind', 'dim', and 'Ind' and mention some of the latest examples that have been given to illustrate the gaps that exist between the various dimensions. Finally, Chapter 4 contains a brief account of a relatively new dimension function "Dim'.

Item Type: Thesis (Masters)
URI: http://research.library.mun.ca/id/eprint/7221
Item ID: 7221
Additional Information: Bibliography: leaves 61-63.
Department(s): Science, Faculty of > Mathematics and Statistics
Date: 1971
Date Type: Submission
Library of Congress Subject Heading: Dimension theory (Topology)

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