Charlieplexing - Revision history

86.188.190.98 at 12:08, 2 December 2014

2014-12-02T12:08:01Z

← Older revision		Revision as of 14:08, 2 December 2014
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	~~In [[mathematics]],~~ the ~~'''poset topology''' associated with a [[partially ordered]] set ''S'' (or [[poset]] for short)~~ is ~~the [[Alexandrov topology]] (open sets are [[upper set]]s) on the poset of [[finite chain]]s of S, ordered by inclusion~~.		The title of the author is Jayson. To play lacross is some thing I truly appreciate performing. Credit authorising is how he tends to make money. Alaska is where I've always been living.<br><br>Feel free to visit my blog real psychics, [http://chungmuroresidence.com/xe/reservation_branch2/152663 visit the following page],

	~~Let V be a set of vertices~~. ~~An [[abstract simplicial complex]] Δ~~ is ~~a set of finite sets of vertices, known as faces <math>\sigma \subseteq V</math>, such that~~
	~~::<math>\forall \rho, \sigma~~. ~~\;\ \rho \subseteq \sigma \in \Delta \Rightarrow \rho \in \Delta</math>~~
	~~Given a simplicial complex Δ as above, we define a (point set) [[topology]] on Δ by letting a subset <math>\Gamma \subseteq \Delta</math> be~~ '~~''closed''' if and only if Γ is a simplicial complex:~~
	::<~~math~~>~~\forall \rho, \sigma. \;\ \rho \subseteq \sigma \in \Gamma \Rightarrow \rho \in \Gamma~~<~~/math~~>
	~~This is the [[Alexandrov topology]] on the poset of faces of Δ.~~

	~~The '''order complex''' associated with a poset~~, S, has the underlying set of S as vertices, and the finite chains (i.e. finite totally-ordered subsets) of S as faces. The poset topology associated with a poset S is the Alexandrov topology on the order complex associated with S.

	~~==See also==~~
	* [[Topological combinatorics]]

	~~==External links==~~
	* [http://~~arxiv~~.~~org~~/~~abs~~/~~math~~/~~0602226 Poset Topology: Tools and Applications~~] ~~Michelle L. Wachs~~, ~~lecture notes IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004)~~

	~~[[Category:General topology]]~~
	~~[[Category:Order theory]]~~

	~~{{topology-stub}}~~

2001:6F8:108F:1:C685:8FF:FE35:F1B: /* Peak current */ remove distracting line break

2014-01-05T11:39:01Z

Peak current: remove distracting line break

← Older revision		Revision as of 13:39, 5 January 2014
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	~~Hello! Allow me begin by saying my title - Ron Stephenson. The preferred pastime~~ for ~~my children and me~~ is ~~dancing and now I'm trying to earn cash with it~~. ~~Delaware has always been my residing place and will never transfer~~. ~~My occupation~~ is a ~~messenger~~.<br><br>~~Feel free to visit my web-site~~; ~~extended car warranty~~ ([http://~~www~~.~~Thehubermangroup.com~~/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/~~60/userId/24292/Default.aspx just click the following article~~])		In [[mathematics]], the '''poset topology''' associated with a [[partially ordered]] set ''S'' (or [[poset]] for short) is the [[Alexandrov topology]] (open sets are [[upper set]]s) on the poset of [[finite chain]]s of S, ordered by inclusion.

			Let V be a set of vertices. An [[abstract simplicial complex]] Δ is a set of finite sets of vertices, known as faces <math>\sigma \subseteq V</math>, such that
			::<math>\forall \rho, \sigma. \;\ \rho \subseteq \sigma \in \Delta \Rightarrow \rho \in \Delta</math>
			Given a simplicial complex Δ as above, we define a (point set) [[topology]] on Δ by letting a subset <math>\Gamma \subseteq \Delta</math> be '''closed''' if and only if Γ is a simplicial complex:
			::<math>\forall \rho, \sigma. \;\ \rho \subseteq \sigma \in \Gamma \Rightarrow \rho \in \Gamma</math>
			This is the [[Alexandrov topology]] on the poset of faces of Δ.

			The '''order complex''' associated with a poset, S, has the underlying set of S as vertices, and the finite chains (i.e. finite totally-ordered subsets) of S as faces. The poset topology associated with a poset S is the Alexandrov topology on the order complex associated with S.

			==See also==
			* [[Topological combinatorics]]

			==External links==
			* [http://arxiv.org/abs/math/0602226 Poset Topology: Tools and Applications] Michelle L. Wachs, lecture notes IAS/Park City Graduate Summer School in Geometric Combinatorics (July 2004)

			[[Category:General topology]]
			[[Category:Order theory]]

			{{topology-stub}}

24.204.205.192: /* Charlieplexing */

2012-09-02T12:05:31Z

Charlieplexing

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Hello! Allow me begin by saying my title - Ron Stephenson. The preferred pastime for my children and me is dancing and now I'm trying to earn cash with it. Delaware has always been my residing place and will never transfer. My occupation is a messenger.<br><br>Feel free to visit my web-site; extended car warranty ([http://www.Thehubermangroup.com/ActivityFeed/MyProfile/tabid/60/userId/24292/Default.aspx just click the following article])