Abstract
Following the necessary algebraic preliminaries, we introduce the homology of a space with coefficients in an arbitrary abelian group. Combined with the results of the previous chapters this establishes the existence of homology theories satisfying the Eilenberg-Steenrod axioms for arbitrary coefficient groups. The corresponding uniqueness theorem is proved in the category of finite CW complexes. Finally, the singular cohomology groups are introduced and shown to satisfy the contravariant analogs of the axioms.
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© 1994 Springer Science+Business Media New York
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Vick, J.W. (1994). The Eilenberg—Steenrod Axioms. In: Homology Theory. Graduate Texts in Mathematics, vol 145. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0881-5_3
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DOI: https://doi.org/10.1007/978-1-4612-0881-5_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6933-5
Online ISBN: 978-1-4612-0881-5
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