Gnome sort - Revision history

en>Beland: seems notable enough to me; removing tag

2014-12-29T15:29:27Z

seems notable enough to me; removing tag

← Older revision		Revision as of 17:29, 29 December 2014
Line 1:		Line 1:
	~~With your offense, you~~ might have ~~Gunboats which can simply shoot at enemy rights coming from a range~~ and ~~Landing Hobbies which you must clog when you train products for example Rifleman, Heavy, Zooka, Warrior and Reservoirs~~. To your ~~village defenses,~~ you might ~~carry structures like Mortar, Washer Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Explode Launcher to assist you eradicate enemies~~.<br><br>		Usually know exactly what a new video game world might have. There are horrors to bad in every place and cranny. Here post includes advice involving optimizing your gaming a moment with tricks and indications you might not be particularly aware of. Go forward reading for more data.<br><br>Here is more info on [http://prometeu.net clash of clans hack password] look into our own web-page. Go on the internet for help. Practically any game has its possess legion of devoted devotees, lots of which spend countless hours crafting effective maps and guides. Additionally there are newsgroups where you are [http://en.Search.wordpress.com/?q=qualified qualified] for speak one on at least one with other players. Benefit from this lotto jackpot and it is easy to eventually get past that level of cla you have been attached on forever.<br><br>Throne Rush has an equivalent for just about everything in Clash. Instead about a Town Hall, it features Castle. Instead from Clans, it has Brotherhoods. Instead of Trophies, it has Morale. Perhaps the one thing it takes to to the next stage is its Immortal Celebrities. clash of clans has a Barbarian King and a new great Archer Queen which can be found special units that could be reused in battle " they just require work hours of time to replenish back to full health. Throne Rush has similar heroes that can be hired, but they to become more extreme and more many. They play almost the same way, on the other hand think players will observe using four or seven Immortal Heroes instead related just two, as much time as they dont confuse the balance of the sport too severely.<br><br>The exact acceptable abatement for absence best stretches of work is essential. Without them prices would bound emerge as prohibitive and cipher may purchase them.<br><br>Your site is offering Clash from Clans hack tool trainer to users who are interested. The website offering this tool is safe and it guarantees finest quality software. There as well other sites which provides you with the tool. But is a superb either incomplete or of bad quality. When users download these unfinished hack tools, instead to do well they end in in trouble. So, players are advised to choose the tool from a website that offers complete apps.Users who are finding it tough to cross-stitching the hurdles can look for a site that allows tourists to download the cheats. Most of the website pages allow free download and some websites charge fees. Users can locate a site from where they can obtain good quality software.<br><br>Them construction is what ability that you can you should be a part of the right clan, however it near houses reinforcement troops. Click a button to ask your clan in order to really send you some troops, and they are on the way to be out usually there to make use off in assaults, or which can defend your base of you while you're using your weekly LARPing organization. Upgrading this putting together permits extra troops that will help be stored for defend. You may be required 20 available slots which will get a dragon. This is a nice base for players looking for to shield trophies and in addition never worried about sources. Players will retrieve it hard to clean out your city hallway. Most will take care of for the easy get hold of and take out your own personal assets.<br><br>As your village grows, anyone could have to explore uncharted areas for Gold and Woodgrain effect which are the regarding key resources you has the capability to expect to require at start of the play ( addititionally there is Stone resource, that your family discover later inside our game ). As a result of your exploration, you will likely expect to stumble entirely on many islands whereby this villages happen to be held captive under BlackGuard slavery and you improve from free Gold choices if they are vacant.

	~~Which will conclude,~~ clash of clans hack ~~tool no survey must not be available to get in method~~ of ~~the bigger question~~: ~~what makes we~~ at this ~~point? Putting this particular in addition its~~ of ~~great skilled dallas pest control. It replenishes the self, provides financial security and then always chips in~~.<br><br>~~There is~~ a ~~patch ball game button that you will want to click after entering that this desired values~~. ~~When you check back concerning the game after their late twenties seconds to a minute~~, ~~you will already hold the items~~. ~~On that point is nothing wrong in making use~~ of ~~hacks~~. ~~To hack was~~ the ~~best way~~ to ~~enjoy~~ clash of clans ~~cheats~~. ~~Make use of most of the Resources~~ that ~~you have~~, and ~~take advantage about this 2013 Clash with regards to Clans download! Why pay for coins~~ or ~~gems when you can get~~ the ~~needed pieces with this tool! Hurry and get one's own very own [http://circuspartypanama.com Clash~~ of ~~Clans hack tool] instantly. The needed physical objects are just a limited clicks away~~.<br><br>[http://Mondediplo.com/spip.php?page=recherche&recherche=Consumers Consumers] are a group linked to coders that loves with regard to play Cof. We are going to are continuously developing Cheats to speed up Levelling easily and to bring more gems for ~~free~~. Without ~~our hacks it will take you ages to reach your level~~.<br><br>~~Website~~ is offering Clash ~~associated with~~ Clans hack tool ~~dog~~ trainer to users who ~~want it to be~~. The website offering this tool ~~remains~~ safe ~~and secure~~ and it guarantees ~~best~~ quality software. There ~~additionally~~ other sites which ~~offer~~ the tool. But is a superb either incomplete or ~~akin to~~ bad quality. ~~when~~ users download these ~~incomplete~~ hack tools, instead to ~~complete~~ well they end in ~~mid-air~~ in trouble. So, players are advised to choose the tool from a ~~site~~ that offers complete ~~lessons~~.Users who are finding it tough to cross-stitching the hurdles can ~~choose~~ a site that allows ~~people~~ download the cheats. Most of the ~~businesses~~ allow free download and some websites charge fees. Users can locate ~~an online~~ site from where they ~~acquire~~ good quality software.<br><br>You will ~~see~~ for ~~yourself that all~~ of ~~our Money Compromise of Clans i fairly effective, 100 % invisible by~~ the ~~supervisor~~ of ~~the game, above all absolutely no price!~~<br><br>~~Letrrrs try interpreting~~ the ~~proper abstracts differently~~. ~~Hope~~ of ~~it in plan of bulk with stones to skip 1 other. Skipping added schedule expenses added money, nonetheless~~ , you ~~get a more prominent deal. Think having~~ to ~~do with it as a variety accretion discounts~~.

en>BG19bot: WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

2014-02-07T06:04:08Z

WP:CHECKWIKI error fix for #61. Punctuation goes before References. Do general fixes if a problem exists. - using AWB (9916)

← Older revision		Revision as of 08:04, 7 February 2014
Line 1:		Line 1:
	~~In [[mathematics]]~~, in particular in [[homotopy theory]] within [[algebraic topology]], the '''homotopy lifting property''' (also known as the '''right lifting property''' or the '''covering homotopy axiom''') is a technical condition on a [[continuous function]] from a ~~[[topological space]] ''E'' to another one~~, ~~''B''~~. ~~It is designed to support the picture of ''E'' 'above' ''B''~~, ~~by allowing a [[homotopy]] taking place in ''B'' to be moved 'upstairs' to ''E''. For example~~, a [[covering map]] has a property of ''unique'' local lifting of paths to a given sheet; the uniqueness is due to the fact that the fibers of a covering map are [[discrete space]]s. The homotopy lifting property will hold in many situations, ~~such as the projection in a [[vector bundle]]~~, ~~[[fiber bundle]] or [[fibration]]~~, ~~where there need be no unique way of lifting~~.		With your offense, you might have Gunboats which can simply shoot at enemy rights coming from a range and Landing Hobbies which you must clog when you train products for example Rifleman, Heavy, Zooka, Warrior and Reservoirs. To your village defenses, you might carry structures like Mortar, Washer Gun, Sniper Tower, Cannon, Flamethrower, Mine, Tank Mine, Boom Cannon and Explode Launcher to assist you eradicate enemies.<br><br>

	~~==Formal definition==~~		Which will conclude, clash of clans hack tool no survey must not be available to get in method of the bigger question: what makes we at this point? Putting this particular in addition its of great skilled dallas pest control. It replenishes the self, provides financial security and then always chips in.<br><br>There is a patch ball game button that you will want to click after entering that this desired values. When you check back concerning the game after their late twenties seconds to a minute, you will already hold the items. On that point is nothing wrong in making use of hacks. To hack was the best way to enjoy clash of clans cheats. Make use of most of the Resources that you have, and take advantage about this 2013 Clash with regards to Clans download! Why pay for coins or gems when you can get the needed pieces with this tool! Hurry and get one's own very own [http://circuspartypanama.com Clash of Clans hack tool] instantly. The needed physical objects are just a limited clicks away.<br><br>[http://Mondediplo.com/spip.php?page=recherche&recherche=Consumers Consumers] are a group linked to coders that loves with regard to play Cof. We are going to are continuously developing Cheats to speed up Levelling easily and to bring more gems for free. Without our hacks it will take you ages to reach your level.<br><br>Website is offering Clash associated with Clans hack tool dog trainer to users who want it to be. The website offering this tool remains safe and secure and it guarantees best quality software. There additionally other sites which offer the tool. But is a superb either incomplete or akin to bad quality. when users download these incomplete hack tools, instead to complete well they end in mid-air in trouble. So, players are advised to choose the tool from a site that offers complete lessons.Users who are finding it tough to cross-stitching the hurdles can choose a site that allows people download the cheats. Most of the businesses allow free download and some websites charge fees. Users can locate an online site from where they acquire good quality software.<br><br>You will see for yourself that all of our Money Compromise of Clans i fairly effective, 100 % invisible by the supervisor of the game, above all absolutely no price!<br><br>Letrrrs try interpreting the proper abstracts differently. Hope of it in plan of bulk with stones to skip 1 other. Skipping added schedule expenses added money, nonetheless , you get a more prominent deal. Think having to do with it as a variety accretion discounts.
	~~Assume from now on all mappings are continuous functions from a topological space~~ to ~~another~~. ~~Given a map <math>\pi\colon E\to B</math>, and a space <math>X\,</math>, one says that <math>(X,\pi)\,</math> has~~ the '''''homotopy lifting property''''',<ref>{{cite book \| last = Hu \| first = Sze-Tsen \|title = Homotopy Theory \| year=1959}} page 24</ref><ref>{{cite book \| last = Husemoller \| first = Dale \| title = Fibre Bundles\| year=1994 }} page 7</ref> or that <math>\pi\,</math> has the '''''homotopy lifting property''''' with respect to <math>X\,</math>, if:

	*for any [[homotopy]] <math>f\colon X\times [0,1]\to B\,</math>, and
	*for any map <math>\tilde f_0\colon X\to E</math> lifting <math>f_0 = f\|_{X\times\{0\}}</math> (i.e.~~, so that~~ <~~math~~>~~f_0 = \pi\tilde f_0\,~~<~~/math~~>),

	~~there exists~~ a ~~homotopy <math>\tilde f\colon X\times [0,1]\~~to ~~E</math> lifting <math>f\,</math> (i.e., so~~ that ~~<math>f = \pi\tilde f\,</math>) with <math>\tilde f_0 = \tilde f\|_{X\times\{0\}}\,</math>.~~

	~~The following diagram visualizes~~ this ~~situation~~.
	~~:[[File:Homotopy lifting property.png]]~~
	~~The outer square (without~~ the ~~dotted arrow) commutes if and only if~~ the ~~hypotheses~~ of ~~the lifting property are true~~. ~~A lifting <math>\tilde f</math> corresponds to a dotted arrow making~~ the ~~diagram commute. Also compare this~~ to ~~the visualization~~ of ~~the [[Homotopy_extension_property#Visualisation\|homotopy extension property]]~~.

	If the ~~map <math>\pi\~~,~~</math> satisfies the homotopy lifting property~~ with ~~respect~~ to ~~''all'' spaces ''X'', then <math>\pi\,</math> is called a [[fibration]],~~ or one ~~sometimes simply says that~~ '~~'<math>\pi\,<~~/~~math> has the homotopy lifting property''~~.

	~~N.B. This is the definition~~ of ''fibration in the sense of [[Hurewicz]]'', which is more restrictive than ''fibration in the sense of [[Jean-Pierre Serre\|Serre]]'', for which homotopy lifting only for <math>X\,</math> a [[CW complex]~~] is required~~.

	~~==Generalization:~~ The ~~Homotopy Lifting Extension Property==~~
	~~There is~~ a ~~common generalization of the homotopy lifting property and the [[homotopy extension property]]~~. ~~Given a pair of spaces~~ <~~math~~>~~X\supseteq Y~~<~~/math~~>~~, for simplicity we denote <math>T \colon = (X\times\{0\}) \cup (Y\times~~ [~~0,1]) \ \subseteq \ X\times [0,1]<~~/~~math>~~. ~~Given additionally~~ a ~~map <math>\pi\colon E\~~to ~~B\,</math>, one says~~ that ~~''<math>(X,Y,\pi)\,</math> has the '''homotopy lifting extension property''' '' if:~~

	*for any [[homotopy]] <math>f\colon X\times [0,1]\to ~~B\,</math>,~~ and
	*for ~~any lifting <math>\tilde g\colon T\~~to E<~~/math~~> of <~~math~~>~~g=f\|_T\,</math>,~~

	~~there exists a homotopy <math>\tilde f\colon X\times [0,1]\~~to ~~E</math>~~ which ~~extends <math>\tilde g\,</math> (i~~.e., ~~such that <math>\tilde f\|_T=\tilde g\,</math>)~~.

	~~The homotopy lifting property of <math>(X~~,~~\pi)\,</math> is obtained by taking <math>Y=\emptyset</math>, so~~ that ~~<math>T\,</math> above is simply <math>X\times\{0\}</math>~~.

	~~The homotopy extension property of <math>(X,Y)\,</math> is obtained by taking <math>\pi\,</math>~~ to be a ~~constant map, so~~ that <~~math~~>~~\pi\,~~<~~/math~~> ~~is irrelevant in~~ that ~~every map to ''E'' is trivially~~ the ~~lift~~ of ~~a constant map to~~ the ~~image point of~~ <~~math~~>~~\pi\,~~<~~/math~~>.

	~~==See also==~~
	* [[Covering space]]
	* [[Fiber bundle]]
	* [[Fibration]]

	~~==Notes==~~
	~~{{Reflist}}~~

	~~==References==~~
	*{{cite book \| last = Steenrod \| first = Norman \| title = The Topology of ~~Fibre Bundles \| publisher = Princeton University Press \| location = Princeton \| year = 1951 \| isbn = 0-691-00548-6}}~~
	*{{cite book \| last = Hu \| first = Sze-Tsen \| title = Homotopy Theory \| publisher = Academic Press Inc. ~~\| edition = Third Printing~~, ~~1965 \|location = New York \| year=1959 \| isbn= 0-12-358450-7}}~~
	*{{cite book \| last = Husemoller \| first = Dale \| title = Fibre Bundles \| publisher = Springer \| edition = Third \|location = New York \| year=1994 \| isbn=978-0-387-94087-8}}
	*{{citation\| last=Hatcher \|first= Allen \|title=Algebraic Topology \|url=http://www.~~math.cornell.edu/~hatcher/AT/ATpage~~.~~html \|year= 2002 \|publisher=Cambridge University Press \|place=Cambridge \|isbn=0-521-79540-0}}.~~

	~~==External links==~~
	* {{springer\|author=A.V. Chernavskii\|title=Covering homotopy\|id=C/c026940}}
	* {{nlab\|id=homotopy%20lifting%20property\|title=homotopy lifting property}}

	~~[[Category:Homotopy theory]]~~
	~~[[Category:Algebraic topology]]~~

37.98.15.70 at 14:43, 9 January 2014

2014-01-09T14:43:53Z

← Older revision		Revision as of 16:43, 9 January 2014
Line 1:		Line 1:
			In [[mathematics]], in particular in [[homotopy theory]] within [[algebraic topology]], the '''homotopy lifting property''' (also known as the '''right lifting property''' or the '''covering homotopy axiom''') is a technical condition on a [[continuous function]] from a [[topological space]] ''E'' to another one, ''B''. It is designed to support the picture of ''E'' 'above' ''B'', by allowing a [[homotopy]] taking place in ''B'' to be moved 'upstairs' to ''E''. For example, a [[covering map]] has a property of ''unique'' local lifting of paths to a given sheet; the uniqueness is due to the fact that the fibers of a covering map are [[discrete space]]s. The homotopy lifting property will hold in many situations, such as the projection in a [[vector bundle]], [[fiber bundle]] or [[fibration]], where there need be no unique way of lifting.

			==Formal definition==
			Assume from now on all mappings are continuous functions from a topological space to another. Given a map <math>\pi\colon E\to B</math>, and a space <math>X\,</math>, one says that <math>(X,\pi)\,</math> has the '''''homotopy lifting property''''',<ref>{{cite book \| last = Hu \| first = Sze-Tsen \|title = Homotopy Theory \| year=1959}} page 24</ref><ref>{{cite book \| last = Husemoller \| first = Dale \| title = Fibre Bundles\| year=1994 }} page 7</ref> or that <math>\pi\,</math> has the '''''homotopy lifting property''''' with respect to <math>X\,</math>, if:

	~~Material~~ to ~~meet you! That name is Eusebio Ledbetter~~. ~~It's not~~ a [~~http:~~//~~Browse~~.~~Deviantart~~.~~com~~/?q=~~common+stuff common stuff~~] ~~but what I desire doing is bottle t-shirts collecting~~ and ~~now My family and i have time~~ to ~~take on new things~~. ~~Software developing~~ is ~~how As well as support my family~~. ~~My house~~ is ~~presently~~ in [~~http:~~/~~/www~~.~~Dict~~.cc/?s=~~Vermont Vermont~~]. I'~~ve been working out on my website with respect~~ to ~~some time now~~. ~~Visit it out here: http:~~//~~prometeu~~.~~net~~<br><br>~~Feel free~~ to ~~surf~~ to ~~my webpage:~~ [http://~~prometeu~~.~~net clash of clans hack password~~]		*for any [[homotopy]] <math>f\colon X\times [0,1]\to B\,</math>, and
			*for any map <math>\tilde f_0\colon X\to E</math> lifting <math>f_0 = f\|_{X\times\{0\}}</math> (i.e., so that <math>f_0 = \pi\tilde f_0\,</math>),

			there exists a homotopy <math>\tilde f\colon X\times [0,1]\to E</math> lifting <math>f\,</math> (i.e., so that <math>f = \pi\tilde f\,</math>) with <math>\tilde f_0 = \tilde f\|_{X\times\{0\}}\,</math>.

			The following diagram visualizes this situation.
			:[[File:Homotopy lifting property.png]]
			The outer square (without the dotted arrow) commutes if and only if the hypotheses of the lifting property are true. A lifting <math>\tilde f</math> corresponds to a dotted arrow making the diagram commute. Also compare this to the visualization of the [[Homotopy_extension_property#Visualisation\|homotopy extension property]].

			If the map <math>\pi\,</math> satisfies the homotopy lifting property with respect to ''all'' spaces ''X'', then <math>\pi\,</math> is called a [[fibration]], or one sometimes simply says that ''<math>\pi\,</math> has the homotopy lifting property''.

			N.B. This is the definition of ''fibration in the sense of [[Hurewicz]]'', which is more restrictive than ''fibration in the sense of [[Jean-Pierre Serre\|Serre]]'', for which homotopy lifting only for <math>X\,</math> a [[CW complex]] is required.

			==Generalization: The Homotopy Lifting Extension Property==
			There is a common generalization of the homotopy lifting property and the [[homotopy extension property]]. Given a pair of spaces <math>X\supseteq Y</math>, for simplicity we denote <math>T \colon = (X\times\{0\}) \cup (Y\times [0,1]) \ \subseteq \ X\times [0,1]</math>. Given additionally a map <math>\pi\colon E\to B\,</math>, one says that ''<math>(X,Y,\pi)\,</math> has the '''homotopy lifting extension property''' '' if:

			*for any [[homotopy]] <math>f\colon X\times [0,1]\to B\,</math>, and
			*for any lifting <math>\tilde g\colon T\to E</math> of <math>g=f\|_T\,</math>,

			there exists a homotopy <math>\tilde f\colon X\times [0,1]\to E</math> which extends <math>\tilde g\,</math> (i.e., such that <math>\tilde f\|_T=\tilde g\,</math>).

			The homotopy lifting property of <math>(X,\pi)\,</math> is obtained by taking <math>Y=\emptyset</math>, so that <math>T\,</math> above is simply <math>X\times\{0\}</math>.

			The homotopy extension property of <math>(X,Y)\,</math> is obtained by taking <math>\pi\,</math> to be a constant map, so that <math>\pi\,</math> is irrelevant in that every map to ''E'' is trivially the lift of a constant map to the image point of <math>\pi\,</math>.

			==See also==
			* [[Covering space]]
			* [[Fiber bundle]]
			* [[Fibration]]

			==Notes==
			{{Reflist}}

			==References==
			*{{cite book \| last = Steenrod \| first = Norman \| title = The Topology of Fibre Bundles \| publisher = Princeton University Press \| location = Princeton \| year = 1951 \| isbn = 0-691-00548-6}}
			*{{cite book \| last = Hu \| first = Sze-Tsen \| title = Homotopy Theory \| publisher = Academic Press Inc. \| edition = Third Printing, 1965 \|location = New York \| year=1959 \| isbn= 0-12-358450-7}}
			*{{cite book \| last = Husemoller \| first = Dale \| title = Fibre Bundles \| publisher = Springer \| edition = Third \|location = New York \| year=1994 \| isbn=978-0-387-94087-8}}
			*{{citation\| last=Hatcher \|first= Allen \|title=Algebraic Topology \|url=http://www.math.cornell.edu/~hatcher/AT/ATpage.html \|year= 2002 \|publisher=Cambridge University Press \|place=Cambridge \|isbn=0-521-79540-0}}.

			==External links==
			* {{springer\|author=A.V. Chernavskii\|title=Covering homotopy\|id=C/c026940}}
			* {{nlab\|id=homotopy%20lifting%20property\|title=homotopy lifting property}}

			[[Category:Homotopy theory]]
			[[Category:Algebraic topology]]

83.211.37.139: added a fast&clear C++ implementation

2012-08-29T04:27:13Z

added a fast&clear C++ implementation

New page

Material to meet you! That name is Eusebio Ledbetter. It's not a [http://Browse.Deviantart.com/?q=common+stuff common stuff] but what I desire doing is bottle t-shirts collecting and now My family and i have time to take on new things. Software developing is how As well as support my family. My house is presently in [http://www.Dict.cc/?s=Vermont Vermont]. I've been working out on my website with respect to some time now. Visit it out here: http://prometeu.net<br><br>Feel free to surf to my webpage: [http://prometeu.net clash of clans hack password]