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Topic: Path connected

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	Connectedness - Wikipedia, the free encyclopedia
		For example, a path connected topological space is simply connected if each loop (path from a point to itself) in it is contractible; that is, intuitively, if there is essentially only one way to get from any point to any other point.
		For example, in graph theory, a connected graph is one from which we must remove at least one vertex to create a disconnected graph.
		The connectivity of a graph is the minimum number of vertices that must be removed, to disconnect it.
	en.wikipedia.org /wiki/Connectedness (765 words)

	PlanetMath: path
		Sometimes, it is convenient to regard two paths or arcs as equivalent if they differ by a reparameterization.
		A path connected space is always a connected space, but a connected space need not be path connected.
		This is version 9 of path, born on 2001-11-17, modified 2004-11-16.
	planetmath.org /encyclopedia/PathConnected.html (231 words)

	Connected space - Wikipedia, the free encyclopedia
		In topology and related branches of mathematics, a connected space is a topological space which cannot be written as the disjoint union of two or more nonempty spaces.
		The connected components of a space are disjoint unions of the path-connected components.
		The closure of a connected subset is connected.
	en.wikipedia.org /wiki/Connected_space (832 words)

	Simply connected space - Wikipedia, the free encyclopedia
		An equivalent formulation is this: X is simply connected if and only if it is path connected, and whenever p : [0,1] → X and q : [0,1] → X are two paths (i.e.: continuous maps) with the same start and endpoint (p(0) = q(0) and p(1) = q(1)), then p and q are homotopic relative {0,1}.
		The long line L is simply connected, but its compactification, the extended long line L* is not (since it is not even path connected).
		If a space X is not simply connected, one can often rectify this defect by using its universal cover, a simply connected space which maps to X in a particularly nice way.
	en.wikipedia.org /wiki/multiply_connected (931 words)

	Simply connected space - Wikipedia, the free encyclopedia
		The opposite is non-simply connected or, in a somewhat old-fashioned term, multiply connected.
		Formally, such a simple object is called a connected space, but for our informal definition, we can just think of a simple object as being an object that's all one piece.
		In theoretical physics, an additional connection is known as a wormhole.
	en.wikipedia.org /wiki/Simply_connected (931 words)

	PlanetMath: example of a connected space that is not path-connected
		This standard example shows that a connected topological space need not be path-connected (the converse is true, however).
		"example of a connected space that is not path-connected" is owned by yark.
		This is version 9 of example of a connected space that is not path-connected, born on 2002-06-10, modified 2005-02-06.
	www.planetmath.org /encyclopedia/ExampleOfAConnectedSpaceWhichIsNotPathConnected.html (256 words)

	PlanetMath: proof that a path connected space is connected
		is connected, this is a contradiction, which concludes the proof.
		"proof that a path connected space is connected" is owned by n3o.
		This is version 3 of proof that a path connected space is connected, born on 2002-06-10, modified 2003-10-04.
	www.planetmath.org /encyclopedia/ProofThatAPathConnectedSpaceIsConnected.html (86 words)

	Inductive load current measuring circuit - Patent 4074175
		The second path from the output of amplifier 74 is by way of a resistor 94 serving as an input resistor to the inverting input of an inverting operational amplifier 96.
		The cathode of thyristor 138 is connected to the cathode of a second controlled rectifier or thyristor 140 and a commutating capacitor 142 is connected between the anodes of the thyristors 138 and 140.
		The cathode of diode 146 is connected to the junction of capacitor 142 and the thyristor 140.
	www.freepatentsonline.com /4074175.html (5609 words)

	Connected space (Site not responding. Last check: 2007-11-06)
		In topology and related branches of mathematics a topological space is said to be connected if it cannot be divided into disjoint nonempty open sets whose union is the entire space.
		A subset of a topological space is said be connected if it is connected carrying subspace topology.
		A space is connected iff it cannot be divided into two nonempty closed sets (since the complement of an open set is closed).
	www.freeglossary.com /Path-connected (686 words)

	Connected space (Site not responding. Last check: 2007-11-06)
		In topology and related branches of mathematics, a topological space is said to be connected if it cannot be divided into two disjoint nonempty open set s whose union is the entire space.
		If X and Y are topological spaces, f is a continuous function from X to Y, and X is connected (respectively, path-connected), then the image f (X) is connected (respectively, path-connected).
		connected connected corporation space between space space between tables space between html space bags space 1999 space picture space simulator retail space outer space space program
	www.serebella.com /encyclopedia/article-Connected_space.html (863 words)

	Semi-locally simply connected (Site not responding. Last check: 2007-11-06)
		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.
		An example of a space that is not semi-locally simply connected is the Hawaiian earring : the union of the circle s 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 locally simply connected.
	www.serebella.com /encyclopedia/article-Semi-locally_simply_connected.html (584 words)

	Sodipodi:
		If the punch entity is a connected path and completely intersects the selected entity, such that the result will be two or more connected paths, then each resultant connected path becomes a separate entity.
		The cropping object must be a connected path (or convertable to a connected path).
		When two or more connected paths are selected, this command produces a new connected path is generated that corresponds to the intersection of all of them.
	www.sodipodi.com /index.php3?section=development/tasks/node_editing_interface (449 words)

	United States Patent: 6,188,211
		The voltage regulator of claim 3, wherein the control electrode of the first positive feedback transistor and the control electrode of the second positive feedback transistor are coupled to the mirror leg at a node connecting the source-drain path of the second MOS transistor and the collector-emitter path of the second bipolar transistor.
		The bases of transistors 16, 18 are connected in common, and to the collector of transistor 16; the collectors of transistors 16, 18 are further connected to the drains of NMOS transistors 20, 22, respectively, which have their sources at ground.
		In this example, the gate of transistor 35 is connected directly to the drain of NMOS transistor 22, and thus in common with the gates of transistors 20, 22.
	users.ece.gatech.edu /~rincon/patents/p6188211.htm (6711 words)

	City of Toronto: PATH - Toronto's downtown walkway
		PATH provides an important contribution to the economic viability of the city's downtown core.
		The average size of a connecting link is 20 metres (66 ft.) long by 6 metres (20 ft.) wide.
		The real growth of PATH began in the 1970s when a tunnel was built to connect the Richmond-Adelaide and Sheraton Centres.
	www.city.toronto.on.ca /path (611 words)

	Reference for NETBuilder Family Software Version 10.1 (Site not responding. Last check: 2007-11-06)
		Specifies the path is connected to an analog modem.
		Specifies the path is connected to a SW56 DSU/CSU.
		Specifies the path is connected to a modem operating in asynch mode.
	support.3com.com /infodeli/tools/bridrout/u_guides/html/nb101/family/ref/path19.htm (289 words)

	HOW THE PETRI-NETS ARE DERIVED FROM TREE-GENERATED ORDER . CONCEQUENCES TO THEIR IMPLEMENTATION .
		path in X from x to y is a continuous map f:[a,b] ®X of some closed real interval into X,such that f(a)=x and f(b)=y.
		A homotopy transformation of a path is a continuous transformation of it that fixes the end points and is realizable in a continuous way inside the topological space.
		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.
	www.softlab.ntua.gr /~kyritsis/PapersInComputerScience/Hrm98Stf.htm (1683 words)

	Connected space - Freepedia (Site not responding. Last check: 2007-11-06)
		Category:TopologyCategory:General topology In topology and related branches of mathematics, a topological space is said to be connected if it cannot be divided into two disjoint nonempty open sets whose union is the entire space.
		A space is connected iff it cannot be divided into two disjoint nonempty closed sets (since the complement of an open set is closed).
		Furthermore, a space is connected iff its only clopen subsets are the empty set and the space itself.
	en.freepedia.org /Connectedness.html (524 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		Furthermore, furthermore, no even-numbered vertex is connected to another larger-numbered vertex (outside of the desired path).
		Vertex 4 is connected to 3 and 5 and smaller numbered vertices that are already used.
		Vertex 2n is connected to (2n-1) and (2n+1) and smaller numbered vertices that are already used, so the path continues...-(2n-1)-2n-(2n+1)-...
	www.mathpuzzle.com /jimboyce.txt (260 words)

	Path connected (Site not responding. Last check: 2007-11-06)
		Equivalently, it can't be divided intotwo disjoint nonempty closed sets (since the complement of an open set is closed).
		The components form a partition of the space (that is, they are disjoint andtheir union is the whole space).
		The topologist's sine curve shown above is an example of a connected space thatis not locally connected.
	www.therfcc.org /path-connected-76535.html (427 words)

	No Title
		Connected vertices: Two vertices a and b are connected if there exists a path from a to b.
		Formally, we want to find a path from ``Ross's wife'' to every other vertex such that the edge labels of the path are in increasing order (since the episode numbers correspond to time).
		If there exists an increasing path from ``Ross's wife'' to another friend then the disease is likely to have been passed to that friend.
	www.cs.rpi.edu /~breime/courses/csci2300/FinalExam (906 words)

	Path connected space (Site not responding. Last check: 2007-11-06)
		Some authorities accept the empty set (with its unique topology) as a connected space, while others donot.
		The space X is said to be path-connected if for any two points x and y in X thereexists a continuous function f from the unit interval [0,1] to X with f(0) = x and f(1) = y.
		The maximal nonempty connected subsets of any topological spaceare called the components of the space.
	www.therfcc.org /path-connected-space-219357.html (427 words)

	M. B. Porter Lectures, 2004-2005 (Site not responding. Last check: 2007-11-06)
		A complex projective variety (or manifold) M is rationally connected when every two points in M lie on a rational curve in M. In these lectures we will explain the strategy for proving an analogous result when the base of the family is a surface.
		In topology any fibration over a circle has a section when the fibres are (path) connected, and a fibration over a 2-sphere has a section when the fibres are 1-connected.
		A rationally connected variety is very roughly a variety on which there lie a lot of rational curves, i.e., there are lots of nonconstant maps from P1 into the variety, in fact enough to connect any two points.
	math.rice.edu /Calendar/porter05.html (512 words)

	Universal Path Spaces (Site not responding. Last check: 2007-11-06)
		The latter hypothesis that each point in the base space has a relatively simply connected open neighborhood---necessary and sufficient for the existence of a simply connected covering space---is abandoned, thus admitting as base even those spaces that contain arbitrarily small essential loops at wild points.
		When the base space is a wild metric 2-complex, the universal path space is simply connected if and only if the fundamental group is an omega-group--a group whose elements acquire non-negative real weights and form countable products of all order-type whenever their weights vanish as their appearance in the order-type deepens.
		The standard features of covering space theory are thus engulfed by the richer features of universal path space theory for a variety of base spaces whose wild local topology prevents the application of traditional covering space theory.
	oregonstate.edu /~bogleyw/research/upsAbs.html (245 words)

	Reference for Enterprise OS Software (Site not responding. Last check: 2007-11-06)
		For path 3, the connector type is a DTE connector type such as RS-232; the ExDevType parameter can be set to Modem, Bri, Sw56, or Async.
		Specifies the path is connected to a synchronous analog modem.
		Specifies the path is connected to an asynchronous analog modem.
	support.3com.com /infodeli/tools/bridrout/u_guides/html/eos1111/family/ref/path19.htm (279 words)

	Boxes and Arrows: We Are All Connected: The Path from Architecture to Information Architecture (Site not responding. Last check: 2007-11-06)
		Connections often extend beyond the design of just a website, to physical spaces and related sites.
		The connection can be physical, financial, emotional or spiritual, but it’s there.
		Knowing that there are connections among the ways people get information, we should at least acknowledge and design for them.
	www.boxesandarrows.com /archives/we_are_all_connected_the_path_from_architecture_to_information_architecture.php (2777 words)

	Re: Lie groups for grunts (Site not responding. Last check: 2007-11-06)
		Call the resulting space X. Then X is connected (it's the closure of the graph, which is connected being the continuous image of a connected space) but not path-connected.
		The two pieces (graph, vertical interval) from which we built X are not connected by any path.
		X is connected if it is not the disjoint union of two open, non-empty subsets U,V < X. (Disjoint means that U and V have no elements in common.
	www.lns.cornell.edu /spr/2000-11/msg0029633.html (455 words)

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