In mathematics, well-behaved topological spaces can be localized at primes, in a similar way to the localization of a ring at a prime.
Localization of a space X is a geometric form of the algebraic device of choosing 'coefficients' in order to simplify the algebra, in a given problem.
We let A be a subring of the rational numbers, and let X be a simply connected CW complex.
Then there is a simply connected CW complex Y together with a map from X to Y such that This space Y is unique up to homotopy equivalence, and is called the localization of X at A.
If A is the localization of Z at a prime p, then the space Y is called the localization of X at p. The map from X to Y induces isomorphisms from the A-localizations of the homology and homotopy groups of X to the homology and homotopy groups of Y.