Topological Pair

In mathematics, more specifically algebraic topology, a pair is shorthand for an inclusion of topological spaces . Sometimes is assumed to be a cofibration. A morphism from to is given by two maps and such that .

Pairs come up mainly in homology theory and cohomology theory, where chains in are made equivalent to 0, when considered as chains in .

Heuristically, one often thinks of a pair as being akin to the quotient space .

There is a functor from spaces to pairs, which sends a space to the pair .