A survey of modern dimension theory

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

[English] PDF (Migrated (PDF/A Conversion) from original format: (application/pdf)) - Accepted Version 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. Download (3MB) [English] PDF - Accepted Version 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. (Original Version)

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'.

Actions (login required)

View Item