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

where the map is induced by the inclusion map and is induced by the inclusion map . The map is called the boundary map.

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

where the map is induced by the inclusion map and is induced by the inclusion map . The map is called the boundary map.

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