In mathematics, more specifically algebraic topology is shorthand for an inclusion of topological spaces is assumed to be a cofibration.

A pair of spaces is an ordered pair where is a topological space and a subspace. The use of pairs of spaces is sometimes more convenient and technically superior to taking a quotient space of by . Pairs of spaces occur centrally in relative homology, homology theory and cohomology theory.

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There is a functor from the category of topological spaces to the category.

A related concept is that of a triple , with . Triples are used in homotopy theory. Often, for a pointed space with basepoint at , one writes the triple as , where .

References

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