122.170.89.231: /* Physical properties */

2014-02-25T06:06:07Z

Physical properties

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	My name is ~~Jamila~~ and ~~I am studying Environmental Management~~ and ~~Arts~~ and ~~Sciences at Piscataway~~ / ~~United States~~.<br><br>~~Here~~ is ~~my web page~~ - [http://www.~~Minijuego~~.~~org~~/~~activity~~/~~p/520087/ Fifa 15 coin generator~~]		:''See also [[Moore space]] for other meanings in mathematics.''
			In [[algebraic topology]], a branch of [[mathematics]], '''Moore space''' is the name given to a particular type of [[topological space]] that is the [[homology theory\|homology]] analogue of the [[Eilenberg–Maclane space]]s of [[homotopy theory]].

			==Formal definition==
			Given an [[abelian group]] ''G'' and an [[integer]] ''n'' ≥ 1, let ''X'' be a [[CW complex]] such that

			:<math>H_n(X) \cong G</math>

			and

			:<math>\tilde{H}_i(X) \cong 0</math>

			for ''i'' ≠ ''n'', where ''H''<sub>''n''</sub>(''X'') denotes the ''n''-th [[Singular homology\|singular homology group]] of ''X'' and <math>\tilde{H}_i(X)</math> is the ''i''th [[reduced homology]] group. Then ''X'' is said to be a '''Moore space'''.

			==Examples==
			*<math>S^n</math> is a Moore space of <math>\mathbb{Z}</math> for <math>n\geq 1</math>.

			*<math>\mathbb{RP}^2</math> is a Moore space of <math>\mathbb{Z}/2\mathbb{Z}</math> (n=1).

			==References==

			*[[Allen Hatcher\|Hatcher, Allen]]. ''Algebraic topology'', Cambridge University Press (2002), ISBN 0-521-79540-0. For further discussion of Moore spaces, see Chapter 2, Example 2.40. A free electronic version of this book is available on the [http://www.math.cornell.edu/~hatcher/ author's homepage].

			[[Category:Algebraic topology]]



			{{topology-stub}}

en>Materialscientist: Reverted edits by Ali.bozorgnia (talk) to last version by DMacks

2012-05-03T06:09:41Z

Reverted edits by Ali.bozorgnia (talk) to last version by DMacks

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My name is Jamila and I am studying Environmental Management and Arts and Sciences at Piscataway / United States.<br><br>Here is my web page - [http://www.Minijuego.org/activity/p/520087/ Fifa 15 coin generator]

Linear low-density polyethylene - Revision history

122.170.89.231: /* Physical properties */

en>Addbot: Bot: Migrating 4 interwiki links, now provided by Wikidata on d:q1863987 (Report Errors)

en>Materialscientist: Reverted edits by Ali.bozorgnia (talk) to last version by DMacks