Definitions
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
- 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.
Read more about this topic: Localization Of A Topological Space
Other articles related to "definitions, definition":
... Some definitions of language, such as early versions of Charles Hockett's "design features" definition, emphasize the spoken nature of language ... Mathematics would not qualify as a language under these definitions, as it is primarily a written form of communication (to see why, try reading Maxwell's ... However, these definitions would also disqualify sign languages, which are now recognized as languages in their own right, independent of spoken language ...
... the need to have precise terminology that cannot be confused with other words or definitions ... He gave emphasis on avoidance of words that have many definitions and compared the language of Scientology with the language of Math and other precise doctrines ... Scientology and Dianetics place a heavy emphasis on understanding word definitions ...
... Although topographic maps of the Chile and Argentina border region which contains the highest peaks are of notoriously poor accuracy, with elevation errors exceeding 100 metres (330 ft) in many cases, the current consensus based on the most recent measurements places Ojos del Salado as the 2nd highest peak and highest volcano in South America, significantly higher than Monte Pissis. ...
... A theoretical (or conceptual) definition gives the meaning of a word in terms of the theories of a specific discipline ... This type of definition assumes both knowledge and acceptance of the theories that it depends on ... An example of a theoretical definition is that of "Heat" in physics, which actually puts forth an entire theory of heat (involving accelerating molecules, etc.) ...
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