Eilenberg–Steenrod Axioms for Homology and Cohomology Theories

  • Mahima Ranjan Adhikari


This chapter presents an approach formulating axiomatization of homology and cohomology theories which makes the subject algebraic topology elegant and provides a quick access to further study. These axioms, now called Eilenberg and Steenrod axioms for homology and cohomology theories, were announced by S. Eilenberg (1915–1998) and N. Steenrod (1910–1971) in 1945 but first appeared in their celebrated book “The Foundations of Algebraic Topology” in 1952.


Cohomology Group Homology Group Homotopy Type Algebraic Topology Axiomatic Approach 
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Copyright information

© Springer India 2016

Authors and Affiliations

  1. 1.Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC)KolkataIndia

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