Axiomatic foundations of homology theory
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This thesis examines systems for homology theory. The Eilenberg-Steenrod axiom system is analyzed in detail, its consistency and categoricity, and certain relationships of equivalence and dependence are proved. Finally, a non-trivial homology theory is constructed satisfying these axioms: the singular homology theory.Then, other axiom systems are introduced and briefly examined: D. Puppe's use of the suspension axiom to replace excision, S. T. Hu's subsequent work on this axiom system, G. M. Kelly's similar approach, P. Shanahan and J. W. T. Youngs' axioms for reduced homology theory, and, lastly, T. R. Brahana's system for local homology theory.
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This work is available on request. You can request a copy at https://library.carleton.ca/forms/request-pdf-copy-thesis
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Copyright © 1969 the author(s). Theses may be used for non-commercial research, educational, or related academic purposes only. Such uses include personal study, research, scholarship, and teaching. Theses may only be shared by linking to Carleton University Institutional Repository and no part may be used without proper attribution to the author. No part may be used for commercial purposes directly or indirectly via a for-profit platform; no adaptation or derivative works are permitted without consent from the copyright owner.
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- 1969
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