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Single-space axioms for homology theory

Published online by Cambridge University Press:  24 October 2008

G. M. Kelly
G. M. Kelly
Affiliation:
University of SydneyNew South Wales
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Extract

Eilenberg and Steenrod(1) give a set of axioms for the homology theory of pairs of spaces and their maps, and prove that these axioms are categorical on triangulable pairs.

Here we give a set of axioms for the homology theory of single spaces and their maps, that is, for absolute rather than relative homology. This axiomatization is shown to be essentially equivalent to that of Eilenberg and Steenrod, the relative homology groups being suitably denned in terms of the absolute groups.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 1 , January 1959 , pp. 10 - 22
Copyright
Copyright © Cambridge Philosophical Society 1959

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References

REFERENCE

(1)Eilenburg, S. and Steenrod, N.Foundations of algebraic topology (Princeton, 1966).Google Scholar