Superactinide - Revision history

en>DePiep: template moved to new name

2014-02-26T22:26:46Z

template moved to new name

← Older revision		Revision as of 00:26, 27 February 2014
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	~~{{Unreferenced\|date=December 2009}}~~		Her title is Felicidad Ahmad. Bookkeeping has been his day occupation for a whilst. Arizona has usually been my living place but my wife wants us to transfer. To play croquet is some thing that I've done for many years.<br><br>Also visit my web page extended auto warranty ([http://Www.themedilawfirm.com/ActivityFeed/MyProfile/tabid/61/UserId/47357/Default.aspx Suggested Browsing])
	~~In [[mathematics]], a [[closure (mathematics)\|closed]] ''n''-[[manifold]] ''N'' [[embedding\|embedded]] in an (''n'' + 1)-manifold ''M''~~ is ~~'''boundary parallel''' (or '''∂-parallel''', or '''peripheral''') if there is an [[Homotopy#Isotopy\|isotopy]] of ''N'' onto~~ a ~~[[Boundary (topology)\|boundary]] [[connected space\|component]] of ''M''~~.

	~~==An example==~~
	~~Consider the [[Annulus (mathematics)\|annulus]] <math>~~I~~\times S^1</math>~~. ~~Let π denote the projection map~~
	:<~~math~~>~~\pi:I\times S^1\rightarrow S^1,\qquad(x,z)\mapsto z.~~<~~/math~~>

	~~If a circle ''S'' is embedded into the annulus so that π [[Restriction#Restrictions and extensions\|restricted]] to ''S'' is a [[bijection]], then ''S'' is boundary parallel.~~ (~~The~~ [~~[Converse (logic)\|converse]] is not true.)~~

	If, on the other hand, a circle ''S'' is embedded into the annulus so that π restricted to ''S'' is not [[Surjection\|surjective]], then ''S'' is not boundary parallel. (Again, the converse is not true.)

	~~[[Image~~:~~Annulus~~.~~circle~~.~~pi 1-injective.png\|thumb\|left\|An example wherein π is not bijective on ''S'', but ''S'' is ∂-parallel anyway~~.]][[Image:Annulus.circle.bijective-projection.png\|thumb\|left\|An example wherein π is bijective on ''S''.]][[Image:Annulus.circle.nulhomotopic.png\|thumb\|left\|An example wherein π is not surjective on ''S''.]]{{Clear}}

	~~{{DEFAULTSORT:Boundary Parallel}}~~
	~~[[Category:Geometric topology]]~~

en>BattyBot: fixed CS1 errors: dates & General fixes using AWB (9846)

2014-01-09T08:05:30Z

fixed CS1 errors: dates & General fixes using AWB (9846)

← Older revision		Revision as of 10:05, 9 January 2014
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	~~Claude~~ is ~~her name and she completely digs~~ that ~~title. He currently lives in Arizona~~ and ~~his mothers and fathers reside close by~~. The ~~favorite pastime for my children and me~~ is ~~dancing and now I~~'~~m attempting~~ to ~~earn cash with it~~. ~~Managing individuals~~ is ~~how I make cash and it~~'~~s something I really appreciate~~.~~<br><br>Take a look at my web~~-~~site~~; [~~http~~:~~//Arcadezeal~~.~~com/profile/brz89 arcadezeal~~.~~com~~]		{{Unreferenced\|date=December 2009}}
			In [[mathematics]], a [[closure (mathematics)\|closed]] ''n''-[[manifold]] ''N'' [[embedding\|embedded]] in an (''n'' + 1)-manifold ''M'' is '''boundary parallel''' (or '''∂-parallel''', or '''peripheral''') if there is an [[Homotopy#Isotopy\|isotopy]] of ''N'' onto a [[Boundary (topology)\|boundary]] [[connected space\|component]] of ''M''.

			==An example==
			Consider the [[Annulus (mathematics)\|annulus]] <math>I\times S^1</math>. Let π denote the projection map
			:<math>\pi:I\times S^1\rightarrow S^1,\qquad(x,z)\mapsto z.</math>

			If a circle ''S'' is embedded into the annulus so that π [[Restriction#Restrictions and extensions\|restricted]] to ''S'' is a [[bijection]], then ''S'' is boundary parallel. (The [[Converse (logic)\|converse]] is not true.)

			If, on the other hand, a circle ''S'' is embedded into the annulus so that π restricted to ''S'' is not [[Surjection\|surjective]], then ''S'' is not boundary parallel. (Again, the converse is not true.)

			[[Image:Annulus.circle.pi 1-injective.png\|thumb\|left\|An example wherein π is not bijective on ''S'', but ''S'' is ∂-parallel anyway.]][[Image:Annulus.circle.bijective-projection.png\|thumb\|left\|An example wherein π is bijective on ''S''.]][[Image:Annulus.circle.nulhomotopic.png\|thumb\|left\|An example wherein π is not surjective on ''S''.]]{{Clear}}

			{{DEFAULTSORT:Boundary Parallel}}
			[[Category:Geometric topology]]

en>Whoop whoop pull up: /* Eka-superactinides */

2012-08-19T04:22:04Z

Eka-superactinides

New page

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