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Topic: Semilocally simply connected

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	Semi-locally simply connected - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-01)
		In mathematics, in particular topology, a topological space X is called semi-locally simply connected if every point x in X has a neighborhood U such that the homomorphism from the fundamental group of U to the fundamental group of X, induced by the inclusion map of U into X, is trivial.
		Evidently, a space that is locally simply connected is semi-locally simply connected.
		An example of a space that is not semi-locally simply connected is the Hawaiian earring: the union of the circles in the Euclidean plane with centers (1/n, 0) and radii 1/n, for n a natural number.
	www.encyclopedia-online.info /Semi-locally_simply_connected (235 words)

	PlanetMath: example of a space that is not semilocally simply connected
		In contrast, the same set endowed with the CW topology is just a bouquet of countably many circles and (as any CW complex) it is semilocaly simply connected.
		"example of a space that is not semilocally simply connected" is owned by mathcam.
		This is version 13 of example of a space that is not semilocally simply connected, born on 2003-02-04, modified 2006-06-06.
	www.planetmath.org /encyclopedia/HawaiianEarrings.html (183 words)

	Semilocally simply connected (Site not responding. Last check: 2007-11-01)
		In mathematics, in particular topology, a topological space X is calledsemi-locally simply connected if every point x in Xhas a neighborhood U such that the homomorphism from the fundamental group of U to the fundamental group of X, induced by the inclusion map of U into X, is trivial.
		An example of a space that is notsemi-locally simply connected is the Hawaiian earring : the union of the circles in the Euclidean plane with centers(1/n, 0) and radii 1/n, for n a natural number.
		It is contractible and therefore semi-locally simply connected, but it is clearly not locallysimply connected.
	www.therfcc.org /semilocally-simply-connected-219360.html (212 words)

	Topology Glossary
		Each connected component is closed, and the set of connected components of a space is a partition of that space.
		A space X is semilocally simply connected if, for every point x in X, there is a neighbourhood U of x such that every loop at x in U is homotopic in X to the constant loop x.
		A space is simply connected if it is path-connected and every loop is homotopic to a constant map.
	www.algebra.com /algebra/about/history/Topology-Glossary.wikipedia (4261 words)

	PlanetMath: semilocally simply connected
		is connected, locally path connected, and semilocally simply connected if and only if it has a universal cover.
		example of a semilocally simply connected space which is not locally simply connected
		This is version 3 of semilocally simply connected, born on 2002-05-17, modified 2003-03-13.
	www.planetmath.org /encyclopedia/Semilocally1Connected.html (119 words)

	Expert About co:Connected
		Connected Geometry is a curriculum development project, funded by the National Science Foundation, designed to help teachers and students engage in meaningful mathematical activity by offering students a chance to understand and appreciate the connections and unifying themes within mathematics, and to build on the connections between students' backgrounds and mathematics.
		A space S is simply connected if it is path-connected and if every map from the 1-sphere to S extends continuously to a map from the 2-disk.
		Jo was connected to a national advice and support helpline for people with eating disorders and was given the number of a counselling service she could call if she felt lonely or depressed.
	www.expertsite.biz /dir/co/connected.htm (1238 words)

	Topology glossary - the free encyclopedia (Site not responding. Last check: 2007-11-01)
		connected if it is not the union of a pair of disjoint nonempty open sets.
		If X is a connected space with more than one point, then a point x of X is a dispersion point if the subspace X − {x} is totally disconnected.
		semilocally simply connected if, for every point x in X, there is a neighbourhood U of x such that every loop at x in U is homotopic in X to the constant loop x.
	www.encyclopedia-of-knowledge.com /default.asp?t=Topology_glossary (3883 words)

	Simply Sleep
		An example of a space that is not semi-locally simply connected is the Hawaiian earring : the unio 6: simply connected, but it is clearly not locally simply connected.
		Simply connected space 4: but a disk and a line are.
		The opposite is '''non-simply connected''' or, in a somewhat old-fashioned term 10: s the loop caught in the object, then it '''is''' simply connected.
	www.lottery-news.net /dust47255-simply_sleep.html (632 words)

	Topology_glossary - The Wordbook Encyclopedia
		Connected: A space is connected if it is not the union of a pair of disjoint nonempty open sets.
		Semilocally simply connected: A space X is semilocally simply connected if, for every point x in X, there is a neighbourhood U of x such that every loop at x in U is homotopic in X to the constant loop x.
		Simply connected: A space is simply connected if it is path-connected and every loop is homotopic to a constant map.
	www.thewordbook.com /Topology_glossary (4574 words)

	search.com - Semi-locally simply connected
		An example of a space that is not semi-locally simply connected is the...
		Anoca.org Semi locally simply connected (semilocallysimplyconnected,semilocally simply connected, semi locallysimply connected,semi locally simplyconnected) In mathematics, in particular topology, a...
		(Redirected from Semilocally simply connected)…An example of a space that is not semi-locally simply connected is the Hawaiian earring: the union of the...
	www.search.com /search?tag=se.fd.box.main.search&q=Semi-locally+simply+connected (355 words)

	Second countable (Site not responding. Last check: 2007-11-01)
		Each connected component is closed, and the set of connected components of aspace is a partition of that space.
		A space X is semilocally simply connected if, for every point x in X, there is aneighbourhood U of x such that every loop at x in U is homotopic in X to theconstant loop x.
		A space is simply connected if it is path-connected and every loopis homotopic to a constant map.
	www.therfcc.org /second-countable-69117.html (3583 words)

	The Homotopy Classes of S1 into s
		Earlier, we defined simply connected as a path connected space where every loop is homotopic to a point, although we didn't use the word "homotopic" in that description.
		A space is locally simply connected if every point x in an open set u is contained in an open set q inside u that is simply connected.
		The space s is semilocally simply connected if, for every point x, there is an open neighborhood q containing x, such that every loop in q is homotopic to a point, using any homotopy in s.
	www.mathreference.com /at,hclass.html (1140 words)

	Semi-locally simply connected (Site not responding. Last check: 2007-11-01)
		Evidently a space that is locally simply is semi-locally simply connected.
		An example of space that is not semi-locally simply connected the Hawaiian earring: the union of the circles in the Euclidean plane with centers (1/ n 0) and radii 1/ n for n a natural number.
		To this consider the cone on the Hawaiian It is contractible and therefore semi-locally simply connected but is clearly not locally simply connected.
	www.freeglossary.com /Semilocally_simply_connected (425 words)

	Topology glossary - InformationBlast
		Each connected component is closed, and the set of connected components of a space forms a partition of that space.
		Equivalently, a space X is semilocally simply connected if and only if, for every point x in X, there is a neighbourhood U of x, such that the group homomorphism of the fundamental group of U at x into the fundamental group of X at x, induced by the inclusion map, is trivial.
		A space X is simply connected if it is path-connected and every loop is homotopic to a constant map.
	www.informationblast.com /Punctured_neighborhood.html (3712 words)

	Topology glossary (Site not responding. Last check: 2007-11-01)
		A space is locally connected if every point has a local consisting of connected neighbourhoods.
		A space is locally simply connected every point has a local base consisting simply connected neighbourhoods.
		A space is simply connected if it is path-connected and every is homotopic to a constant map.
	www.freeglossary.com /Contractible (3572 words)

	HOW THE PETRI-NETS ARE DERIVED FROM TREE-GENERATED ORDER . CONCEQUENCES TO THEIR IMPLEMENTATION .
		simply connected if it is path-connected space (that is any two points can be connected with a continuous path) and if p
		A universal covering tree of a graph G, covers any other covering graph of G. Remark 15 The flow-charts of programs are finite connected graphs with two pointed vertices called the beginning and the end and with all their branches being oriented.
		The relation is simply the precedence of vertices from the next vertices (in direction from a root to the leaves of the tree if it is finite).
	www.softlab.ntua.gr /~kyritsis/PapersInComputerScience/Hrm98Stf.htm (1683 words)

	Dogpile - Web Search: Semi-locally simply connected
		PlanetMath: example of a space that is not semilocally
		An example of a space that is not semilocally
		connected then the functor F is an equivalence of...
	www.dogpile.com /info.dogpl.sbox/search/redir.htm?qcat=web&qkw=Semi-locally+simply+connected (197 words)

	The Hawaiian Earring
		Travel around one of these circles and find a loop that is not homotopic to a point.
		In the next section we'll see that a locally simply connected space always has a universal cover.
		Since the hawaiian earring is not locally simply connected, it might not have a universal cover.
	www.mathreference.com /at-cov,haw.html (723 words)

	Qwika - 拓撲學術語
		Path-connected component。 path-connected component 是指極大的非空道路連通子空間。空間中的 path-connected components 組成空間的一個分割，這個分割比 connected components 組成的分割要細。空間 X 的 path-connected components 所組成的集合我們記做 π
		Spatial □ X Center if wilfully □ X All some □□territory U Causes all U Center X On loop all □in X On □loop with □, □I □□□□is often spatial □□ Semilocally simply connected.
		All □□□passes spatial □and all parts □□□passes spatially □all is semilocally simply connected.
	wikipedia.qwika.com /zh2en/%E6%8B%93%E6%92%B2%E5%AD%B8%E8%A1%93%E8%AA%9E (2600 words)

	Semi locally simply connected Article, Semilocallysimplyconnected Information (Site not responding. Last check: 2007-11-01)
		An example of a space that is notsemi-locally simply connected is the Hawaiian earring : the union of the circles in the Euclidean plane with centers (1/n, 0) and radii 1/n, for n a natural number.Give this space the subspace topology.
		It is contractible and thereforesemi-locally simply connected, but it is clearly not locally simply connected.
		We take no responsibility for the content, accuracy and use of this article.
	www.anoca.org /space/spaces/semi_locally_simply_connected.html (244 words)

	AMCA: Unique path lifting and the shape group by Hanspeter Fischer (Site not responding. Last check: 2007-11-01)
		A path connected and locally path connected space X has a universal covering space if and only if it is semilocally simply connected.
		Even if p: tilde{X}-->X does not cover X evenly, it always allows for lifts of maps f :Y-->X whose domain Y is simply connected and locally path connected.
		For many spaces, semilocally simply connected or not, this homomorphism is known to be injective: for example, for all subsets of the Euclidean plane, for all 1-dimensional compacta, as well as for boundaries of certain Coxeter groups.
	at.yorku.ca /c/a/n/y/20.htm (225 words)

	SEMI-LOCALLY CONECTOU SIMPLESMENTE (Site not responding. Last check: 2007-11-01)
		A propriedade do connectivity semi-locally simples é mais fraca do que aquela do connectivity simples local.
		Para ver isto, considerar o cone no earring havaiano.
		It is licensed under the GNU free documentation license.
	www.faktoport.com /wiki/pt/se/Semilocally%20conectou%20simplesmente.htm (225 words)

	Simply Whispers (Site not responding. Last check: 2007-11-01)
		1) " Simply" -- As it applies to Simply Whispers
		Simply Mad About The Mouse 1: '''''Simply Mad Ab...
		2) " Whispers" -- As it applies to Simply Whispers
	www.elusiveeye.com /side3671-simply-whispers.html (635 words)

	Eas Simply Gain (Site not responding. Last check: 2007-11-01)
		1) " Eas" -- As it applies to Eas Simply Gain
		2) " Simply" -- As it applies to Eas Simply Gain
		3) " Gain" -- As it applies to Eas Simply Gain
	www.elusiveeye.com /side15595-eas-simply-gain.html (629 words)

	Resource guide explores the variety of news and information sources (Site not responding. Last check: 2007-11-01)
		Mourning rituals in America were directly influenced by those in England and During the Victorian era children and even babies were put into mourning.
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		A compact set in a Hausdorff space is closed · free vector space over a set example of a semilocally simply connected space which is not locally.
	www.proyectourbania.org /forum/thread42.html (19382 words)

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	Deu -> Engl. \| Bereich Wortlisten \| Mathlab.de (Site not responding. Last check: 2007-11-01)
		lokal wegzusammenhängend - locally arcwise connected, locally pathwise connected
		semilokal einfach zusammenhängend - semilocally simply connected separabelseparable
		Skalarprodukt - dot product, inner product, scalar product
	www.mathlab.de /mathematik/liste_dengl.html (303 words)

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