**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"

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**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

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**Definitions**- South America

... 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.) ...

### Famous quotes containing the word definitions:

“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?

There have been many *definitions* of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”

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—Pamela Patrick Novotny (20th century)