Pyramorphix - Revision history

145.18.225.199: /* corrected the spelling of Pyramorphix (was Pyramophix) */

2014-07-14T07:42:46Z

corrected the spelling of Pyramorphix (was Pyramophix)

← Older revision		Revision as of 09:42, 14 July 2014
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	The writer's ~~name~~ is ~~Christy Brookins~~. I am truly ~~fond of handwriting but~~ I ~~can~~'~~t make it my occupation really.~~ Mississippi ~~is where his house is~~. ~~Invoicing~~ is what ~~I do~~.<br><br>~~Also visit my web page~~: ~~psychics online -~~ [http://~~www.zavodpm~~.~~ru/blogs~~/~~glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going www.zavodpm~~.ru] -		The writer's title is Andera and she thinks it seems fairly good. To climb is something I truly appreciate performing. I've usually loved residing in Mississippi. Office supervising is what she does for a residing.<br><br>My website :: real psychic ([http://clothingcarearchworth.com/index.php?document_srl=441551&mid=customer_review simply click the up coming site])

en>Mvpo666 at 18:06, 28 February 2014

2014-02-28T18:06:48Z

← Older revision		Revision as of 20:06, 28 February 2014
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	~~In [[mathematics]], particularly in [[differential topology]], the '''preimage theorem''~~' is ~~a theorem concerning the preimage of particular points in a [[manifold]] under the action of a [[smooth map]]~~.		The writer's name is Christy Brookins. I am truly fond of handwriting but I can't make it my occupation really. Mississippi is where his house is. Invoicing is what I do.<br><br>Also visit my web page: psychics online - [http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going www.zavodpm.ru] -

	~~==Statement~~ of ~~Theorem==~~

	''~~Definition~~.~~'' Let <math>f: X \to Y\,\!</math> be a smooth map between manifolds~~. ~~We say that a point <math>y \in Y</math>~~ is ~~a ''regular value of f'' if for all <math>x \in f^{-1}(y)~~<~~/math~~> ~~the map~~ <~~math~~>~~df_x~~: ~~T_xX \to T_yY\,\!</math> is~~ [~~[surjective map\|surjective]]. Here, <math>T_xX\,\!<~~/~~math> and <math>T_yY\,\!<~~/~~math> are the [[tangent space]]s of X and Y at the points x and y~~.


	~~''Theorem~~.~~'' Let <math>f: X \to Y\,\!<~~/~~math> be a smooth map, and let <math>y \in Y<~~/~~math> be a regular value of ''f''~~. ~~Then <math>f^{-1}(y) = \{x \in X : f(x) =y \}</math> is a submanifold of X~~. ~~Further, if <math>y</math> is in the image of ''f'', the [[codimension~~]~~] of this manifold in X is equal to the dimension of Y, and the [[tangent space]] of <math>f^{-1}(y)</math> at a point <math>x</math> is <math>Ker(df_x)</math>.~~

	~~{{topology~~-~~stub}}~~
	~~[[Category:Theorems in differential topology]]~~

86.177.223.50 at 16:50, 16 December 2013

2013-12-16T16:50:58Z

← Older revision		Revision as of 18:50, 16 December 2013
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	~~Golda is what~~'~~s created on my beginning certificate even though it~~ is ~~not~~ the ~~title on my beginning certification~~. ~~Distributing manufacturing is where my primary earnings comes from and it~~'~~s some thing I truly appreciate~~. It'~~s not~~ a ~~typical thing but what I like doing~~ is ~~to climb but I don~~'~~t have the time lately. I~~'~~ve always loved living~~ in ~~Mississippi~~.<br><br>~~My blog~~ ..~~. real [http~~://~~www~~.~~010~~-~~5260-5333.com/index.php?document_srl~~=~~1880&mid~~=~~board_ALMP66 online psychic] [http:~~/~~/isaworld~~.~~pe.kr~~/~~?document_srl=392088 love psychic readings~~] - ~~[http:~~//~~www.weddingwall~~.~~com.au/groups/easy~~-~~advice-for-successful-personal-development-today/ Read the Full Report~~] -		In [[mathematics]], particularly in [[differential topology]], the '''preimage theorem''' is a theorem concerning the preimage of particular points in a [[manifold]] under the action of a [[smooth map]].

			==Statement of Theorem==

			''Definition.'' Let <math>f: X \to Y\,\!</math> be a smooth map between manifolds. We say that a point <math>y \in Y</math> is a ''regular value of f'' if for all <math>x \in f^{-1}(y)</math> the map <math>df_x: T_xX \to T_yY\,\!</math> is [[surjective map\|surjective]]. Here, <math>T_xX\,\!</math> and <math>T_yY\,\!</math> are the [[tangent space]]s of X and Y at the points x and y.


			''Theorem.'' Let <math>f: X \to Y\,\!</math> be a smooth map, and let <math>y \in Y</math> be a regular value of ''f''. Then <math>f^{-1}(y) = \{x \in X : f(x) =y \}</math> is a submanifold of X. Further, if <math>y</math> is in the image of ''f'', the [[codimension]] of this manifold in X is equal to the dimension of Y, and the [[tangent space]] of <math>f^{-1}(y)</math> at a point <math>x</math> is <math>Ker(df_x)</math>.

			{{topology-stub}}
			[[Category:Theorems in differential topology]]

en>Olsonist: Rubik's Cube not Rubik's cube

2012-04-05T19:09:46Z

Rubik's Cube not Rubik's cube

New page

Golda is what's created on my beginning certificate even though it is not the title on my beginning certification. Distributing manufacturing is where my primary earnings comes from and it's some thing I truly appreciate. It's not a typical thing but what I like doing is to climb but I don't have the time lately. I've always loved living in Mississippi.<br><br>My blog ... real [http://www.010-5260-5333.com/index.php?document_srl=1880&mid=board_ALMP66 online psychic] [http://isaworld.pe.kr/?document_srl=392088 love psychic readings] - [http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ Read the Full Report] -