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	Atlas (topology) - Wikipedia, the free encyclopedia
		This definition of atlas is exactly analogous to the non-mathematical meaning of atlas.
		Each individual map in an atlas of the world gives a neighborhood of each point on the globe that is homeomorphic to the plane.
		By definition, a smooth differentiable structure (or differential structure) on a manifold M is such a maximal atlas of charts, all related by smooth coordinate changes on the overlaps.
	en.wikipedia.org /wiki/Chart_%28topology%29 (412 words)

	Atlas (topology) -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-06)
		In (The configuration of a communication network) topology, an atlas describes how a complicated (An area reserved for some particular purpose) space is glued together from simpler pieces.
		At the minimum, we require that the composite of one chart with the inverse of another be a homeomorphism (known as a change of coordinates), but we usually impose stronger requirements, such as (A texture without roughness; smooth to the touch) smoothness.
		Each individual map in an atlas of the world gives a neighborhood of each point on the globe that is homeomorphic to the (A carpenter's hand tool with an adjustable blade for smoothing or shaping wood) plane.
	www.absoluteastronomy.com /encyclopedia/a/at/atlas_(topology).htm (417 words)

	Atlas (topology) (Site not responding. Last check: 2007-11-06)
		Each individual map in an atlas the world gives a neighborhood of each on the globe that is homeomorphic to plane.
		By definition a smooth differentiable structure (or differential structure) on a manifold M is such a maximal atlas of all related by smooth coordinate changes on overlaps.
		Atlas' music is a fine blend of western dance music and arab music (whatever that maybe).
	www.freeglossary.com /Local_coordinate_system (704 words)

	Science Online Center - Math - Topology - General_Topology
		Thus a general theme in topology is to test the extent to which the axioms force the kind of structure one expects to use and then, as appropriate, introduce other axioms so as to better match the intended application.
		Members of the Analytic Topology Research Group at the Mathematical Institute, University of Oxford, are working on a range of topological topics, which include: topology of metric spaces, generalised metric spaces, continua, function spaces, hyperspaces, topological algebra, set theoretic methods in topology, and applications of topology to computer science and the theory of differential equations.
		General topology is that branch of pure mathematics that concerns itself with the nature of continuity.
	www.science-online-center.com /math/topology/general_topology (1129 words)

	[No title]
		Topology Glossary Mainly extracted from (a) UC Davis Math:Profile Glossary (http://www.math.ucdavis.edu/profiles/glossary.html) by Greg Kuperberg (http://www.math.ucdavis.edu/profiles/kuperberg.html), and (b) Topology Atlas Glossary (http://www.achilles.net/~mtalbot/TopoGloss.html).
		An early result in topology states that every closed 3-manifold (closed meaning that the manifold is finite and connected but has no boundary) has a Heegaard splitting and a resulting description in terms of a Heegaard diagram, which describes how the two handlebodies are glued together.
		In 3-dimensional topology, a surface in a 3-manifold with the property that no essential circle in the surface bounds a disk in the manifold.
	www.ornl.gov /sci/ortep/topology/defs.txt (5717 words)

	Atlas (topology) - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-06)
		At the minimum, we require that the composite of one chart with the inverse of another be a homeomorphism (known as a change of coordinates), but we usually impose stronger requirements, such as smoothness.
		maximal atlas: an atlas of charts refines another one if it adds charts (in such a way that the overlap functions remain compatible).
		The existence of maximal atlases, that cannot further be refined, follows from Zorn's lemma.
	encyclopedia.worldsearch.com /chart_(topology).htm (322 words)

	Fiber bundle - Wikipedia, the free encyclopedia
		In mathematics, in particular in topology, a fiber bundle (or fibre bundle) is a space which locally looks like a product of two spaces but may possess a different global structure.
		Fiber bundles generalize vector bundles, where the main example is the tangent bundle of a manifold.
		Since bundles do not in general have globally-defined sections, one of the purposes of the theory is to account for their existence.
	www.wikipedia.org /wiki/Fibre_bundle (1166 words)

	An Atlas of Cyberspaces - Topology Maps
		A diagram of the topology of all the network connections in the 6Bone, an experimental international IPv6 testbed network.
		A topology cybermap of search results from the AltaVista search engine using their LiveTopics system.
		The link map was created by Eva Ekeblad and her paper "The emergence and decay of multilogue: self-regulation of a scholarly mailinglist." give more details on this research.
	www.cybergeography.org /atlas/more_topology.html (567 words)

	Cover (topology) - Wikipedia, the free encyclopedia
		Covers are commonly used in the context of topology.
		If the set X is a topological space, we say that C is an open cover if each of its members are open sets (i.e.
		If C is a cover of X then a subcover of C is a subset of C which still covers X.
	www.wikipedia.org /wiki/Cover+(topology) (344 words)

	Mesothelioma - Atlas (Site not responding. Last check: 2007-11-06)
		An atlas is usually based on a grid of fixed intervals of distance or degrees latitude and longitude.
		ATLAS, a man who held up the heavens and was not even a preacher.
		Atlas King of Mauritania in Africa, fabled to have supported the world upon his shoulders.
	www.mesothelioma.me.uk /asbestos+Atlas.html (397 words)

	54: General topology
		Topology is the study of sets on which one has a notion of "closeness" -- enough to decide which functions defined on it are continuous.
		Since the axioms of topology are stated in terms of subsets of X, it should be no surprise that one branch of topology is closely related to set theory, particularly "descriptive set theory".
		For example, if we would like to know which spaces might have a topology which is consistent with a metric, we know individual points must be closed; the axiom that this is true (the "T_1" axiom) is but one of a number of separation axioms.
	www.math.niu.edu /~rusin/known-math/index/54-XX.html (2431 words)

	topology -- Encyclopædia Britannica
		Topology, the youngest and most sophisticated branch of geometry, focuses on the properties of geometric objects that remain unchanged upon continuous deformation—shrinking, stretching, and folding, but not tearing.
		Basis elements are half-open intervals open on the right—that is, sets of the form [p, q] in which p, q are points of the horizontal line with p to the left of q, each set consisting of p and all points strictly between p and q.
		His original contributions to the fields of probability theory and topology have had a significant impact on modern physics, chemistry, biology, and cybernetics.
	www.britannica.com /eb/article-9108691 (802 words)

	An Atlas of Cyberspaces - Topology Maps
		It was created using an automatic network discovery tool called Mercator developed as part of the Scan project by Ramesh Govindan, Anoop Reddy and colleagues, at the Information Sciences Institute, USA.
		The map above left shows the ATM network circa September 1996, while the map on the right is a schematic map of the backbone topology of SuperJANET III from early 1998.
		The topology map below shows the new SuperJANET4 backbone, as of March 2001.
	www.cybergeography.org /atlas/topology.html (668 words)

	Atlas (topology) (Site not responding. Last check: 2007-11-06)
		At the minimum, we require that the composite of one chartwith the inverse of another be a homeomorphism (known as a change of coordinates, but we usually impose strongerrequirements, such as smoothness.
		Each individual map in an atlas of the world gives a neighborhood of each point on theglobe that is homeomorphic to the plane.
		The choice of atlas for a space is not unique, but we can always choose a unique maximal atlas: an atlas ofcharts refines another one if it adds charts (in such a way that the overlap functions remain compatible).
	www.therfcc.org /atlas-topology--69121.html (307 words)

	NAMEzero - Web Directory: Browse
		Algebraic Topology Discussion List - The primary functions of this list are: providing abstracts of papers posted to the Hopf archive, providing information about topology conferences, and serving as a forum for topics related to algebraic topology.
		TTT on WWW - The Transpennine Topology Triangle is a topology seminar partially supported by the London Mathematical Society with vertices at Leicester, Manchester and Sheffield.
		Topology of Manifolds: Supersymmetry and QFT - This is the web resource page for a course taught by John Morgan in Fall 1997 at Columbia University.
	kevdb.infospace.com /info.direct/kevdb?KCFG=dmoz&otmpl=dmoz/dmoz-out.htm&qk=50&qcat=Top/Science/Math/Topology (301 words)

	Matematik 3GT E03 (Site not responding. Last check: 2007-11-06)
		The short answer is: Topology is the study of continuity.
		History of Topology if you want to know where it all came from.
		Topology Course som de ser det i Irland or Nord Irland.
	www.math.ku.dk /~moller/e03/3gt/3gt.html (631 words)

	An Atlas of Cyberspaces
		This is an atlas of maps and graphic representations of the geographies of the new electronic territories of the Internet, the World-Wide Web and other emerging Cyberspaces.
		Some of the maps you will see in the Atlas of Cyberspaces will appear familiar, using the cartographic conventions of real-world maps, however, many of the maps are much more abstract representations of electronic spaces, using new metrics and grids.
		If you would like to be kept informed of updates to the Atlas of Cyberspaces please register to receive the free Cyber-Geography Research Bulletin.
	www.cybergeography.org /atlas/atlas.html (235 words)

	The Math Forum - Math Library - Topology
		A multi-purpose center for electronic distribution of information related to topology, the mathematical study of surfaces, sometimes called "rubber sheet geometry" because topologists consider geometric figures as though they were drawn on infinitely stretchable rubber sheets.
		A short article designed to provide an introduction to general topology, the study of sets on which one has a notion of "closeness" - enough to decide which functions defined on it are continuous.
		Thus it is a kind of generalized geometry (we are still interested in spheres and cubes, for example, but we might consider them to be "the same", yet distinct from a bicycle tire, which has a "hole") or a kind of generalized analysis...
	mathforum.org /library/topics/topology (2459 words)

	Protein Topology WWW site
		The topology cartoon for the variable domain of the heavy chain of the antibody fragment structure with Brookhaven code 6fab, along with the three-dimensional structure for comparison.
		The atlas of topology cartoons was generated from the version of the PDB current on 1st July 1997.
		Each cartoon in the atlas was checked manually with the 3D structure of the protein, and the success rate in producing satisfactory cartoons was found to be 82%.
	www.tops.leeds.ac.uk /emblnet.html (1639 words)

	55: Algebraic topology
		Algebraic topology is the study of algebraic objects attached to topological spaces; the algebraic invariants reflect some of the topological structure of the spaces.
		Apart from homology groups and their kin, the principal algebraic tool used in topology is the set of homotopy groups of a space, and related concepts; in particular this includes the fundamental group (pi_1(X)) of a space.
		The tools of algebraic topology, when developed in isolation or for applications to other fields such as ring theory, give rise to homological algebra and category theory; this is the proper framework for comparing different algebraic tools.
	www.math.niu.edu /~rusin/known-math/index/55-XX.html (2581 words)

	Open Directory - Science: Math: Topology: General Topology (Site not responding. Last check: 2007-11-06)
		Oxford Analytic Topology Research Group - Research interests: topology of metric spaces, generalised metric spaces, continua, function spaces, hyperspaces, topological algebra, set theoretic methods in topology, and applications of topology to computer science and the theory of differential equations.
		Textbook in Problems on Elementary Topology - The core of the book is the material included usually into the Topology part of the two year geometry course in the Mathematical Department of St. Petersburg University.
		Topology - Descriptions and illustrations of several Topological and Differential Geometry related notions.
	dmoz.org /Science/Math/Topology/General_Topology (420 words)

	Atlas: The Topology of Compact Groups by Sidney A. Morris (Site not responding. Last check: 2007-11-06)
		Atlas: The Topology of Compact Groups by Sidney A. Morris
		The purpose of this talk is to use the known topological group structure theory to describe to general topologists the topology of compact groups.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cait-31.
	atlas-conferences.com /cgi-bin/abstract/cait-31 (196 words)

	moon atlas \| New resources for moon atlas (Site not responding. Last check: 2007-11-06)
		Moon Atlas (Rukl, A.) The German version of Rukl's Moon Atlas was used.
		Atlas (moon) [Categories: Saturn's moons] Atlas Discovery Discovered by R. Terrile Discovered in 1980 Quick Facts about: Orbit The (usually elliptical) path described by one celestial body in its...
		One of these, reported earlier, populates the same orbit as the small moon Atlas; others lie in various gaps in the rings and may indicate the presence of tiny embedded moons coincident with them or...
	www.1st-atlas.info /moonatlas (1250 words)

	John J. Schommer (Site not responding. Last check: 2007-11-06)
		The Topology Atlas recently celebrated the one-year anniversary of its service to the topology community.
		With the handling of abstracts now almost entirely automated, the Abstract Section of the Atlas is poised to cover more than just a few major conferences and seminars.
		This short talk will describe how abstracts are processed, and how the Atlas can assist future conference organizers in the production of their conference abstract booklets.
	www.utm.edu /staff/jschomme/topology/c/a/a/n/07.htm (124 words)

	IST Intermon
		Atlas of maps and graphic representations of the geographies of the new electronic territories of the Internet, the World-Wide Web and other emerging Cyberspaces”.
		Based on active probing of the network, it discovers network connectivity (topology), measures round trip time and record dynamic changes of topologies.
		For backbone topology visualization they use some graph layout code written by Bill Cheswick from Bell Labs and Hal Burch from CMU.
	www.ist-intermon.org /topics/topology_map.html (459 words)

	Novell Documentation: ZENworks for Servers 3 - Managing the Atlas
		When ZfS is first installed, the server module of the Atlas Manager is automatically installed on the management server, and the client module of the Atlas Manager is installed on ConsoleOne.
		The Atlas Manager on the management server creates a system atlas and provides a graphical view of the database at the console.
		The Atlas Manager on the server reads the database and provides two different views of the database at ConsoleOne: the Console view and Atlas view.
	www.novell.com /documentation/zfsi/zfs_admin/data/holbg528.html (933 words)

	Research
		Topology is one of the most beautiful branches of mathematics.
		There are several definitions and descriptions of what topology is. To put it shortly topology studies the most general aspects of shape in mathematics.
		The branch of topology that deals with notions important in classical analysis, functional analysis, set theory, algebra and other disciplines is called general topology.
	math.tntech.edu /alex/oldpage/res.html (513 words)

	An Atlas of Cyberspaces- ISP Backbone Maps
		The map above shows the topology of the network in May 1999.
		Unfortunately, the map is no longer available, but details on current topology is here.
		The topology of this new backbone network, as of December 2001 is show opposite.
	www.cybergeography.org /atlas/isp_maps.html (429 words)

	Search: Topology - Info.co.uk
		Linda Belau Petar Ramadanovic Topologies of Trauma: Essays on the Limit of Knowledge and Memory (Contemporary Theory) Linda Belau Petar Ramadanovic Topologies of Trauma: Essays on the Limit of Knowledge and Memory (Contemporary Theory) Belau Linda Ramadanovic Petar Linda Belau Petar Ramadanovic...
		Topology is the mathematical study of the properties that are preserved through deformations, twistings, and stretchings of objects.
		We are able to do this through extensive research of various circuit topologies, together with specially selected components from around the world.
	dpxml.infospace.com /infocom.uk/results?otmpl=dog/webresults.htm&qkw=Topology&CMP=KNC-3LS480536328&infoad=1 (350 words)

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