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	Simply Connected
		A topological space is simply connected if it is path connected, and it has no holes.
		The plane is simply connected, but the plane without the origin is not.
		Unless otherwise stated, simply connected refers to paths and circles, regardless of the dimension of the containing space.
	www.mathreference.com /top,sconnect.html (214 words)

	PlanetMath: simply connected
		A topological space is said to be simply connected if it is path connected and the fundamental group of the space is trivial (i.e.
		Cross-references: group, fundamental group, path connected, topological space
		This is version 4 of simply connected, born on 2001-11-16, modified 2002-02-12.
	planetmath.org /encyclopedia/SimplyConnected.html (70 words)

	PlanetMath: locally simply connected
		is said to be locally simply connected at
		is said to be locally simply connected if it is locally simply connected at every point.
		This is version 3 of locally simply connected, born on 2003-02-05, modified 2004-03-02.
	www.planetmath.org /encyclopedia/LocallySimplyConnected.html (65 words)

	Definition of simply connected - Merriam-Webster Online Dictionary
		Learn more about "simply connected" and related topics at Britannica.com
		Find more about "simply connected" instantly with Live Search
		See a map of "simply connected" in the Visual Thesaurus
	www.m-w.com /dictionary/simply+connected (56 words)

	Tetrad
		simply connected) shapes which are placed without overlapping in such a way that each shape shares some boundary (of
		simply connected tetrads consisting of four congruent shapes.
		It is still an unsolved problem whether a simply connected congruent tetrad can be
	karl.kiwi.gen.nz /prtetrad.html (647 words)

	Kids.Net.Au - Encyclopedia > Simply connected
		For instance, a doughnut is not simply connected, but a ball (even a hollow one) is. A circle is not simply connected but a disk and a line is.
		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.
	www.kids.net.au /encyclopedia-wiki/si/Simply_connected (473 words)

	Simply connected space - Biocrawler (Site not responding. Last check: )
		For instance, a doughnut (with hole) is not simply connected, but a ball (even a hollow one) is. A circle is not simply connected but a disk and a line are.
		Note that the image of a simply connected set under a continuous function need not to be simply connected.
		The Riemann mapping theorem states that any non-empty open simply connected subset of C (except for C itself) can be conformally and bijectively mapped to the unit disk.
	www.biocrawler.com /encyclopedia/Simply_connected_space (815 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		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.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=connectedness (809 words)

	Simply Wireless - Wireless Network Specialist
		A wireless network means the laptops are instantly connected when they walk into class, and even on their way to class.
		Compared to traditional cable, wireless offers a robust, secure, scalable and economical means to connect teaching staff and students to the information they need in their day to day lives.
		Simply Wireless has a wealth of experience in the Educational Market, and is currently working with some of the leading Universities, Post Primary Schools and MBA college's in Australia.
	www.simplywireless.com.au /education.htm (993 words)

	The Tetratorus and Other Multi-Layered Polyhedra
		Similarly, the edge of "h" is connected to the edge of "i".
		This last connection obviously can't be achieved in 3D without the surface intersecting itself, but just as with the Klein bottle we are free to imagine an embedding in a higher dimensional space that allows us to adjoin all the edges as described.
		Notice that the intrinsic connections between all the faces of this "wound up" version are identical to the connections of the "flat" version, including the alignment of the adjoining edges of the "l" and "a" faces.
	www.mathpages.com /home/kmath517.htm (2330 words)

	The Riemann Mapping Theorem and the Uniformization Theorem (Site not responding. Last check: )
		The case of simply connected domains is answered by Riemann Mapping Theorem.
		Thus we have that there are two classes of simply connected domains in the complex plane, namely the complex plane and the unit disc.
		The classification of simply connected Riemann surfaces is given by the Uniformization theorem.
	www.math.tifr.res.in /~pablo/teichmuller/node12.html (295 words)

	[No title]
		The most striking technique ap- plies if G is simply connected and gives a formula for the order of ZG in terms of the exponents of the Weyl group W of G; the formula is derived by studying certain special elements in W called Coxeter ele- ments.
		In this case the universal cover of G is a simply connected almost simple compact Lie group K, and G is isomorphic to K=A for some finite subgroup A of ZK.
		Theorem.Q Any connected p-compact group can be written as a product X x iYi, where X is a p-compact group of Lie type, and each Yi is a simply connected almost simple p-compact group which is not of Lie type.
	hopf.math.purdue.edu /Dwyer-Wilkerson/center-calc/center-calc.txt (9062 words)

	The Cauchy-Goursat Theorem
		A domain that is not simply connected is said to be a multiply connected domain.
		Figure 6.16 illustrates uses of the terms simply connected and multiply connected.
		We can extend Theorem 6.6 to multiply connected domains with more than one "hole.'' The proof, which is left for the reader, involves the introduction of several cuts and is similar to the proof of Theorem 6.6.
	math.fullerton.edu /mathews/c2003/CauchyGoursatMod.html (740 words)

	Connected Corporation \| Sign Up
		Connected Data Backup Service includes a small piece of software that is easy to install on your home PC.
		To run the setup program, simply go to the location on your disk where you downloaded the setup file during step 2, and double-click the file.
		If you simply lose data files that previously have been backed up, and your Connected software is still intact, you can simply run Connected, then retrieve the lost files.
	www.connected.com /stanford/plandetails_dtabk_sign.asp (945 words)

	Types of Mazes
		The ideal multiply-connected maze has no dead ends at all, and is called a "Braid maze." The Amazeing Art mazes are multiply-connected mazes.
		A mind-bending maze whose underlying topology is unusual (non-Euclidean) and which has edges that connect with one another.
		For example, quite a few outdoor mazes are multiply-connected weave mazes, because they have passages that connect back and forth as well as passages that go over or under other passages (via bridges, tunnels, etc.).
	www.amazeingart.com /maze-faqs/maze-types.html (622 words)

	James Tauber : Number of Connected One-Dimensional Manifolds
		I'm confused by the third statement as I would have thought that the half-open interval (0,1] and the circle are both connected one-dimensional manifolds but that neither of them are homeomorphic to either the open or closed intervals.
		Perhaps whoever wrote that was thinking of simply connected manifolds (where 'simply connected' is defined differently from 'connected'); the circle is not simply connected.
		RxR is simply connected, RxR minus the center is not.
	jtauber.com /blog/2005/09/22/number_of_connected_one-dimensional_manifolds (488 words)

	Simply Connected, Mu-Ency at MROB (Site not responding. Last check: )
		A set of points is simply connected if it is connected and its complement is also connected.
		A set with "holes" is not simply connected.
		From the Mandelbrot Set Glossary and Encyclopedia, © 1987-2006 Robert P. Munafo.
	www.mrob.com /pub/muency/simplyconnected.html (63 words)

	The Homotopy Category of Simply Connected 4-Manifolds - Cambridge University Press
		The Homotopy Category of Simply Connected 4-Manifolds - Cambridge University Press
		Including a complete list of references for the text, the book appeals to researchers and graduate students in topology and algebra.
		The homotopy category of simply connected 4-manifolds; 3.
	www.cambridge.org /us/catalogue/catalogue.asp?isbn=0521531039 (164 words)

	Simply Connected
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	www.simplyconnected.com (56 words)

	Double node neighborhoods and families of simply connected 4-manifolds with b(+)=1
		Double node neighborhoods and families of simply connected 4-manifolds with b(+)=1
		Printing Tips: Select 'print as image' in the Acrobat print dialog if you have trouble printing.
		R Fintushel and Ronald J. Stern, "Double node neighborhoods and families of simply connected 4-manifolds with b(+)=1" (2006).
	repositories.cdlib.org /postprints/1237 (92 words)

	Web Site Design, Calgary, AB Affordable, Low Cost Web Design by Simply Effective - Portfolio
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		Simply Effective Web Design Inc. 2006 © All Rights Reserved.
	www.simplyeffective.ca /html/portfolio.html (336 words)

	Semi locally simply connected (Site not responding. Last check: )
		That is, every loop in U can be deformed to apoint.
		The property of semi-locally simple connectivity is weaker than that of local simple connectivity.
		In the theory of covering spaces, a space has a universal cover if and only if it is path-connected, locallypath-connected, and semi-locally simply connected.
	www.therfcc.org /semi-locally-simply-connected-35904.html (212 words)

	Math Forum Discussions
		>to imply simply connected, but I can't prove it.
		"Simply connected" isn't the same as "path connected" - it is
		more than 1 point, which implies it is path connected.
	mathforum.org /kb/thread.jspa?threadID=1436323&messageID=5055439 (192 words)

	My Wife Is Switching to the Mac
		To copy her documents to the Mac mini, I simply connected to the network share, courtesy of Mac OS X's integrated Windows networking, and copied her documents into her new Documents folder.
		Simply because I was tired of 'opening the hood.' The thing works.
		Of course I was not connected to the company network, but I merely copied all my Word and Excel documents to a CD, popped it into my PC and was up and running in less than 5 minutes.
	www.connectedhomemag.com /HomeOffice/Articles/Index.cfm?ArticleID=48887 (8252 words)

	Reading Room \| Simply Connected, an original science fiction story
		The upper stairwell connecting the ground floor of the house to the upper story and the attic was situated next to the kitchen; as they passed by, Jim noticed Deb and Stephie talking to the washing machine.
		I must have switched the connections in the `D' and `E' panels.
		I'll bet the radio is connected to the dryer." Ralph strode over to six metal boxes mounted on the wall.
	www.xenite.org /reading_room/simply_connected.htm (7014 words)

	Definition of Semi-locally simply connected
		That is, every loop in U can be deformed to a point.
		It is contractible and therefore semi-locally simply connected, but it is clearly not locally simply connected.
		In the theory of covering spaces, a space has a universal cover if and only if it is path-connected, locally path-connected, and semi-locally simply connected.
	www.wordiq.com /definition/Semi-locally_simply_connected (274 words)

	[math/0510599] The stable mapping class group of simply connected 4-manifolds
		We consider mapping class groups \Gamma(M) = pi_0 Diff(M fix \partial M) of smooth compact simply connected oriented 4-manifolds M bounded by a collection of 3-spheres.
		We show that if M contains CP^2 (with either orientation) as a connected summand then \Gamma(M) is independent of the number of boundary components.
		We also comment on versions of these results for simply connected spin 4-manifolds.
	www.arxiv.org /abs/math.gt/0510599 (224 words)

	15a
		be a smooth, projective geometryicall connected, geometrically simply connected surface.
		Point of the talk: It should be possible to do descent on (at least some) surfaces with nonzero geometric genus.
		is a geometrically simply connected surface, and the Tate conjecture is true, then the
	www.aimath.org /WWN/qptsurface2/articles/html/15a (241 words)

	Unramified cohomology of classifying varieties for exceptional simply connected groups (Site not responding. Last check: )
		Let BG be a classifying variety for an exceptional simple simply connected algebraic group G. We compute the degree 3 unramified Galois cohomology of BG with values in (Q/Z)'(2) over an arbitrary field F. Combined with a paper by Merkurjev (Ann.
		Sup., 4-e serie, 35 (2002), 445--476), this completes the computation of these cohomology groups for G semisimple simply connected over all fields.
		These computations provide another example of a simple simply connected group G such that BG is not stably rational.
	www.mathcs.emory.edu /~skip/ur/ur.html (145 words)

	Caerdroia - Maze Typology
		If the wall surrounding the goal of a maze is connected to the perimeter of the maze at the entrance, the maze can always be solved by keeping one hand in contact with the wall, however many detours that may involve.
		It was not until the early nineteenth century that the principle of isolating the goal of the maze from the perimeter to defeat the "hand-on-wall" method and increase the level of difficulty was truly understood.
		The introduction of the third dimension allows the islands of a multiply- connected maze to be totally isolated from each other, with the only link via a bridge.
	www.labyrinthos.net /typology_m.htm (707 words)

	Maths holy grail could bring disaster for internet \| The Guardian \| Guardian Unlimited
		It turned out to be possible to prove the Poincaré conjecture in unimaginable worlds, where objects have four or five or more dimensions, but not with three.
		"The one case that is really of interest because it connects with physics, is the one case where the Poincaré conjecture hasn't been solved," said Keith Devlin, of Stanford University in California.
		2 Poincaré conjecture The surface of an apple is simply connected.
	www.guardian.co.uk /uk_news/story/0,3604,1298728,00.html (1315 words)

	simply. The American Heritage® Dictionary of the English Language: Fourth Edition. 2000.
		In an unambiguous way; clearly: explained the concept simply.
		Merely; only: It is simply a matter of time.
		Frankly; candidly: You are, quite simply, the best candidate for the job.
	www.bartleby.com /61/94/S0419400.html (102 words)

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