Axiomatic foundations of homology theory

Creator: 

Gibson, Mary Elizabeth

Date: 

1969

Abstract: 

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.

Subject: 

Homology Theory
Axioms

Language: 

English

Publisher: 

Carleton University

Thesis Degree Name: 

Master of Science: 
M.Sc.

Thesis Degree Level: 

Master's

Thesis Degree Discipline: 

Mathematics

Parent Collection: 

Theses and Dissertations

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