The reason to do this was in line with an idea of making topology, more precisely algebraic topology, more geometric. 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. Instead of that, the localization can be applied to the space X, directly, giving a second space Y.
Adams, Frank (1978), Infinite loop spaces, Princeton, N.J.: Princeton University Press, pp. 74–95, ISBN0-691-08206-5
Sullivan, Dennis P. (2005), Ranicki, Andrew (ed.), Geometric Topology: Localization, Periodicity and Galois Symmetry: The 1970 MIT Notes(PDF), K-Monographs in Mathematics, Dordrecht: Springer, ISBN1-4020-3511-X
localization, topological, space, mathematics, well, behaved, topological, spaces, localized, primes, similar, localization, ring, prime, this, construction, described, dennis, sullivan, 1970, lecture, notes, that, were, finally, published, sullivan, 2005, rea. In mathematics well behaved topological spaces can be localized at primes in a similar way to the localization of a ring at a prime This construction was described by Dennis Sullivan in 1970 lecture notes that were finally published in Sullivan 2005 The reason to do this was in line with an idea of making topology more precisely algebraic topology more geometric 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 Instead of that the localization can be applied to the space X directly giving a second space Y Definitions editWe 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 Y is A local this means that all its homology groups are modules over A The map from X to Y is universal for homotopy classes of maps from X to A local CW complexes 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 See also editCategory Localization mathematics Local analysis Localization of a category Localization of a module Localization of a ring Bousfield localizationReferences editAdams Frank 1978 Infinite loop spaces Princeton N J Princeton University Press pp 74 95 ISBN 0 691 08206 5 Sullivan Dennis P 2005 Ranicki Andrew ed Geometric Topology Localization Periodicity and Galois Symmetry The 1970 MIT Notes PDF K Monographs in Mathematics Dordrecht Springer ISBN 1 4020 3511 X nbsp This commutative algebra related article is a stub You can help Wikipedia by expanding it vte Retrieved from https en wikipedia org w index php title Localization of a topological space amp oldid 1214297586, wikipedia, wiki, book, books, library,
