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# Topic: Topology glossary

 Topology - Wikipedia, the free encyclopedia Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. Topology is concerned with the study of the so-called topological properties of figures, that is to say, properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms). In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories. en.wikipedia.org /wiki/Topology   (1344 words)

 Topology glossary - Wikipedia, the free encyclopedia This is a glossary of some terms used in the branch of mathematics known as topology. Algebraic topology is the study of topologically invariant abstract algebra constructions on topological spaces. The weak topology on a set, with respect to a collection of functions from that set into topological spaces, is the coarsest topology on the set which makes all the functions continuous. en.wikipedia.org /wiki/Topology_glossary   (4512 words)

 Learn more about Topology in the online encyclopedia.   (Site not responding. Last check: 2007-11-06) In architecture, topology is a term used to describe spatial effects which can not be described by topography, i.e., social, economical, spatial or phenomenological interactions. In mathematics, topology is a branch concerned with the study of topological spaces. Wiring and computer network topologies are discussed in network topology.) Roughly speaking, topology is the study of geometric objects without considering their dimensions. www.onlineencyclopedia.org /t/to/topology_1.html   (1178 words)

 Encyclopedia: Topological space The Zariski topology is a purely algebraically defined topology on the spectrum of a ring or an algebraic variety. In topology and related fields of mathematics, a discrete space is a particularly simple example of a topological space or similar structure, one in which the points are isolated from each other in a certain sense. In topology and related branches of mathematics, a topological space X is said to be disconnected if it is the union of two disjoint nonempty open sets. www.nationmaster.com /encyclopedia/Topological-space   (6141 words)

 Topology - Encyclopedia.WorldSearch   (Site not responding. Last check: 2007-11-06) Topology (Greek topos = place and logos = word) is a branch of mathematics concerned with the study of topological spaces. The term "topologie" was introduced in German in 1847 by Johann Benedict Listing (1808-1882) in "Vorstudien zur Topologie," Vandenhoeck und Ruprecht, Göttingen, pp. "Topology", its English form, was introduced in print by Solomon Lefschetz in 1930 to replace the earlier name "analysis situs." The separate status of the topologist, a specialist in topology, was probably established from around 1920. encyclopedia.worldsearch.com /topology.htm   (1315 words)

 UC Davis Math: Glossary   (Site not responding. Last check: 2007-11-06) 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 topology, a number, polynomial, or other quantity associated to a topological object such as a knot or 3-manifold which depends only on the underlying object and not on its specific description or presentation. In topology, the terms circle and sphere refer to topological objects and not geometric ones, so that the surface of an egg shape is a sphere. www.math.ucdavis.edu /profiles/glossary.html   (9932 words)

 Topology glossary   (Site not responding. Last check: 2007-11-06) This is a glossary of some terms used in the branch of mathematics knownas topology. Compact-open topology The compact-open topology on the set C(X,Y) of all continuous maps between two spaces X and Y is defined as follows: given a compact subsetK of X and an open subset U of Y, let V(K, U) denote the set ofall maps f in C(X, Y) such that f(K) is contained in U. The weak topology on a set, with respect to a collection of functions from that set into topologicalspaces, is the coarsest topology on the set which makes all the functions continuous. www.therfcc.org /topology-glossary-35846.html   (3583 words)

 Topology glossary   (Site not responding. Last check: 2007-11-06) This is a glossary of some terms in the branch of mathematics known as topology. Although there is no clear distinction different areas of topology this glossary focuses on general topology and on definitions that are fundamental a broad range of areas. The weak topology on a set with respect to collection of functions from that set into spaces is the coarsest topology on the which makes all the functions continuous. www.freeglossary.com /Local_base   (3572 words)

 topology manifold   (Site not responding. Last check: 2007-11-06) Topology Glossary Mainly extracted from (a) UC Davis Math:Profile Glossary (http://www... Redirected from Symplectic topology) In mathematics, a symplectic manifold is a smooth manifold equipped with a... Attracting Manifold for a Viscous Topology Transition Attracting Manifold for a Viscous Topology Transition An analytical method is developed describing the approach to a finite-time singularity associated with collapse of a narrow fluid... www.maps-universe.com /articles/34/topology-manifold.html   (426 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). 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. round In topology, the terms circle and sphere refer to topological objects and not geometric ones, so that the surface of an egg shape is a sphere. www.ornl.gov /sci/ortep/topology/defs.txt   (5717 words)

 Topology glossary   (Site not responding. Last check: 2007-11-06) Although there is no clear distinction between different areas of topology, this glossary focuses primarily on general topology and on definitions that are fundamental to a broad range of areas. A collection of open sets is a subbase (or subbasis) for a topology if every open set in the topology is a union of finite intersections of sets in the subbase. If B is any collection of subsets of a set X, the topology on X generated by B is the smallest topology containing B; this topology consists of all unions of finite intersections of elements of B. www.sciencedaily.com /encyclopedia/topology_glossary   (3712 words)

 [No title]   (Site not responding. Last check: 2007-11-06) Topology is also concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called Seven Bridges of Königsberg is regarded as one of the first results on geometry that does not depend on any measurements, i.e., one of the first topological results. Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of en-cyclopedia.com /wiki/Topology   (1239 words)

 Global Village | Glossary A network topology in which nodes are connected to a single cable with terminators at each end. A network topology in which nodes are connected in a closed loop; no terminators are required because there are no unconnected ends. A network topology in which nodes are connected to a common device such as hub or concentrator. www.globalvillage.com /technologies/glossary.html   (3688 words)

 Gourt :: Science :: Math :: Topology 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. 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. 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. science.gourt.com /Math/Topology.html   (325 words)

 Miscy Directory - Top > Science > Math > Topology   (Site not responding. Last check: 2007-11-06) Topics in Mathematics - Topology - In the Mathematics Archives at University of Tennessee, Knoxville. 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. 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. dir.miscy.com /Science/Math/Topology   (283 words)

 Definition: network topology Note 1: Two networks have the same topology if the connection configuration is the same, although the networks may differ in physical interconnections, distances between nodes, transmission rates, and/or signal types. star topology: A network topology in which peripheral nodes are connected to a central node, which rebroadcasts all transmissions received from any peripheral node to all peripheral nodes on the network, including the originating node. tree topology: A network topology that, from a purely topologic viewpoint, resembles an interconnection of star networks in that individual peripheral nodes are required to transmit to and receive from one other node only, toward a central node, and are not required to act as repeaters or regenerators. www.atis.org /tg2k/_network_topology.html   (568 words)

 Insurance Glossary -- Recommendations and Resources   (Site not responding. Last check: 2007-11-06) It seems that the current glossary is evolving into a "general topology" glossary (i.e. de:Glossar A core glossary is a simple glossary or defining dictionary which enables definition of other concepts, especially for newcomers to a language or field of study. The word ''glossary'' itself is derived from the Greek ''glossa'' (γλωσσα) meaning "tongue". www.becomingapediatrician.com /health/79/insurance-glossary.html   (909 words)

 EEA - Glossary - topology Topology is a branch of geometry concerned with the study of topological spaces. (The term topology is also used for a set of open sets used to define topological spaces). Most of the GIS (Geography Information System) layers use simple topology: point, line, polygon and region. glossary.eea.eu.int /EEAGlossary/T/topology   (84 words)

 What is topology? - A Word Definition From the Webopedia Computer Dictionary bus topology: All devices are connected to a central cable, called the bus or backbone. ring topology : All devices are connected to one another in the shape of a closed loop, so that each device is connected directly to two other devices, one on either side of it. Ring topologies are relatively expensive and difficult to install, but they offer high bandwidth and can span large distances. www.webopedia.com /TERM/t/topology.html   (237 words)

 J. Roque Dias • TRANSLATION LINKS • Page 2 Glossary of the terms that are used whenever pollutants are discussed Glossary of Terms for Agriculture, Agricultural Economics and Precision Farming (German<>English) Glossary of Whisky and Distillation (by The Celtic Whisky Compagnie) www.jrdias.com /jrd-links-2.html   (1229 words)

 topology - OneLook Dictionary Search Topology : A Glossary of Mathematical Terms [home, info] Phrases that include topology: bus topology, ring topology, star topology, network topology, logical topology, more... Words similar to topology: topologies, topologist, analysis situs, more... www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=topology   (403 words)

 Topology Glossary   (Site not responding. Last check: 2007-11-06) Glossary of Terms: UMTS - Universal Mobile Telecommunications System is the... Beware, some authors, especially analystss, use the term weaker topology. Beware, some authors, especially analystss, use the term stronger topology. www.wikiverse.org /topology-glossary   (3377 words)

 [No title]   (Site not responding. Last check: 2007-11-06) Mainly extracted from (a) UC Davis Math:Profile Glossary In 3-dimensional topology, a surface in a 3-manifold with the property topology of the space of possible inputs or outputs or the space of www.mcs.vuw.ac.nz /~hong/defs.html   (4965 words)

 Geometry Glossary on Almondnet   (Site not responding. Last check: 2007-11-06) Glossary of differential geometry and topology Glossary of field theory Glossary... Comprehensive glossary of the terms used in fusion research. Links in italics are to documents outside of this glossary, and will open in a new browser window... www.free-range-pork.co.uk /pork/geometry_glossary.html   (363 words)

 Topology glossary Information   (Site not responding. Last check: 2007-11-06) A function from one space to another is closed if the [[image (mathematics)image]] of every closed set is closed. A function from one space to another is open if the [[image (mathematics)image]] of every open set is open. If X is a space, Y is a set, and f : X → Y is any [[surjectionsurjective]] function, then the quotient topology on Y induced by f is the finest topology for which f is continuous. www.articleshead.com /show_article/topology-glossary   (3967 words)

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