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Long Exact Sequence of a Pair Axiom

One of the Eilenberg-Steenrod axioms. It states that, for every pair (X,A), there is a natural long exact sequence

...->H_n(A)->H_n(X)->H_n(X,A)->H_(n-1)(A)->...,

where the map H_n(A)->H_n(X) is induced by the inclusion map A->X and H_n(X)->H_n(X,A) is induced by the inclusion map (X,phi)->(X,A). The map H_n(X,A)->H_(n-1)(A) is called the boundary map.

See also

Eilenberg-Steenrod Axioms, Long Exact Sequence

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Cite this as:

Weisstein, Eric W. "Long Exact Sequence of a Pair Axiom." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LongExactSequenceofaPairAxiom.html

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