Topological pair
From Wikipedia, the free encyclopedia
 |
This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (August 2008) |
 |
It has been suggested that this article or section be merged with pair of spaces. (Discuss) |
In mathematics, more specifically algebraic topology, a pair (X,A) is short-hand for an inclusion of topological spaces 
. Sometimes i is assumed to be a cofibration. A morphism from (X,A) to (X',A') is given by two maps 
and 
such that 
.
Pairs come up mainly in homology theory and cohomology theory, where chains in A are made equivalent to 0, when considered as chains in X.
Heuristically, one often thinks of a pair (X,A) as being akin to the quotient space X / A.
There is a functor from spaces to pairs, which sends a space X to the pair 
.
