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Topic: Cover (topology)

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	ESRI News -- ArcNews Summer 2002 Issue -- ArcGIS 8.3 Brings Topology to the Geodatabase
		Topology rules, when applied to geographic features or feature classes in a geodatabase, enable GIS users to model such spatial relationships as connectivity (are all of my road lines connected?) and adjacency (are there gaps between my parcel polygons?).
		Topology is also used to manage the integrity of coincident geometry between different feature classes (e.g., are the coastlines and country boundaries coincident?).
		A topology is a set of integrity rules for the spatial relationships along with a few important properties: a cluster tolerance, feature class ranks (for coordinate accuracy), errors (rule violations), and any exceptions to the rules you've defined.
	www.esri.com /news/arcnews/summer02articles/arcgis83-brings.html (2242 words)

	Topology Encyclopedia (Site not responding. Last check: )
		Topology (Greek topos, "place," and logos, "study") is a branch of mathematics that is an extension of geometry.
		The most basic division within topology is into point-set topology, which investigates such concepts as compactness, connectedness, countability, and algebraic topology, which investigates such concepts as homotopy, homology, and knot theory.
		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.
	www.hallencyclopedia.com /topic/Topology.html (1819 words)

	Cover (topology) - Wikipedia, the free encyclopedia
		In mathematics, a cover of a set X is a collection of subsets C of X whose union is X.
		Covers are commonly used in the context of topology.
		An open cover of X is said to be locally finite if every point of X has a neighborhood which intersects only finitely many sets in the cover.
	en.wikipedia.org /wiki/Open_cover (362 words)

	Topology Summary
		Topology is sometimes called "rubber-sheet geometry" because if a shape is drawn on a rubber sheet (like a piece of a balloon), then all of the shapes you can make by stretching or twisting—but never tearing—the sheet are considered to be topologically the same.
		Topology has sometimes been called rubber-sheet geometry, because it does not distinguish between a circle and a square (a circle made out of a rubber band can be stretched into a square) but does distinguish between a circle and a figure eight (you cannot stretch a figure eight into a circle without tearing).
		However, Lacan's use of topology, like his use of algebra, does not meet the standards of rigour normally evinced by a mathematical discipline, and should be seen more as an analogy (the value of which is left to the reader to decide upon) than as a branch of applied mathematics.
	www.bookrags.com /Topology (6184 words)

	Cover - Encyclopedia, History, Geography and Biography
		Cover (law), a remedy for the breach of a contract for the receipt of goods.
		Cover (topology), the mathematical concept of a collection of subsets of a set whose union is the whole set
		Cover (intelligence), the purported occupation or purpose of an agent.
	www.arikah.com /encyclopedia/Cover (195 words)

	Topology : TopOlogy
		Topology is a term used in architecture to describe spatial effects which can not be described by topography, i.e., social, economical, spatial or phenomenological interactions.
		Topology is that branch of mathematics concerned with the study of topological spaces.
		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.
	www.termsdefined.net /to/topology.html (1222 words)

	Glossary of Topology Terms
		A covering transformation is a homeomorphism of a covering space with itself that preserves the covering map.
		The covering map p is the covering of a sheet by its blanket.
		The metric d gives rise to a topology on P; a basis for this topology is the collection of sets { q: d(p,q)0.
	cage.rug.ac.be /~hvernaev/TopoGloss.html (2536 words)

	Home Page
		Topology is "rubber geometry," technically, the mathematics of bicontinuous one-to-one transformations of a set of points comprising a so-called space.
		Associated with the points is a family of "open sets" that cover the space, like the response fields that constitute neighborhoods of the actual neurons in the brain.
		This is where algebraic topology comes in, in the form of simplicial topology and fibrations.
	home.att.net /~topologicalpsychology/index.htm (1169 words)

	Reference.com/Encyclopedia/Paracompact space
		A cover of a set X is a collection of subsets of X whose union is X.
		A refinement of a cover of a space X is a new cover of the same space such that every set in the new cover is a subset of some set in the old cover.
		A star refinement of a cover of a space X is a new cover of the same space such that, given any point in the space, the star of the point in the new cover is a subset of some set in the old cover.
	www.reference.com /browse/wiki/Paracompact (1026 words)

	[No title]
		The topology P consists of the elements in O and the complements of closed subsets as neighborhoods of that point.
		Hausdorff topology +------------------------------------------------------------ The Hausdorff topology is a metric on the set of closed bounded subsets of a complete metric space.
		induced topology +------------------------------------------------------------ The induced topology on a subset A of X, where (X,T) is a topological spoace is the the topological space (A, Y cap A _Y in T).
	www.math.harvard.edu /~knill/sofia/data/topology.txt (1652 words)

	Topology
		You may update topology of the source cover copy the source cover to a target cover and update the target cover's topology only.
		In the topology dialogs, this option is only available for coverages, whose User-IDs are being used as primary key between location data and the feature attribute tables.
		Open the cover properties dialog to edit the properties of the currently selected cover.
	members.aol.com /jbhlp1/afhlp/html/earc3vzt.htm (975 words)

	Topological Properties
		T is the topology on H. The subsets of H in T are open sets.
		Quaternions form a topology because they are what mathematicians call a metric space, since q* q evaluates to a real positive number or equals zero only if q is zero.
		Topology plus causality could be the key for subdividing different regions of physics.
	www.theworld.com /~sweetser/quaternions/intro/topology/topology.html (1623 words)

	[No title]
		The topology P consists of the elements in O and the complements of closed subsets as neighborhoods of that point.
		Hausdorff topology +------------------------------------------------------------ The Hausdorff topology is a metric on the set of closed bounded subsets of a complete metric space.
		induced topology +------------------------------------------------------------ The induced topology on a subset A of X, where (X,T) is a topological spoace is the the topological space (A, Y cap A _Y in T).
	abel.math.harvard.edu /~knill/sofia/data/topology.txt (1652 words)

	Topology \| Browse \| All Categories \| page #1 \| gigapedia.org
		Even though the book has no figures (as one would expect from a topology book), almost every detail is covered and there are not obscure parts in the proofs.
		Many books of topology cover just that, but this one goes all the way to generalizations in other areas as is appropriate for topologists.
		Topology is about geography, shapes and sizes, folding and stretching/squeezing without breaking.
	gigapedia.org /item.id:61801,title:topology,cat_id:,cat_page:.html (849 words)

	Topology glossary (Site not responding. Last check: )
		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.
		If T is a topology on a space X and if A is a subset of X then the subspace topology on A induced by T consists of all intersections of open in T with A.
		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)

	cover - Wiktionary
		According to the Oxford English Dictionary, the original sense of the verb and noun cover was hide from view as in its cognate covert.
		Except in the limited sense of cover again, the word recover is unrelated and is cognate with recuperate.
		(topology) A set (more often known as a family) of sets, whose union contains the given set.
	en.wiktionary.org /wiki/cover (360 words)

	Phone-man's Home Phone Wiring Advice Page - Routing of Your Phone Cable
		In a ring topology, all jacks are on one cable that forms a "loop", routed through the house from one jack to the next, with both "ends" connected at the NID.
		In a bus topology, all jacks are on one cable that starts at the NID and is routed through the house from one jack to the next and terminates at the last desired jack location.
		Hybrid topologies normally were initially installed as one of the basic topologies and are the result of additions.
	www.homephonewiring.com /route.html (1466 words)

	Basic Topology Home Page (Site not responding. Last check: )
		Sections 7 and 10 are the relevant section of the text, though I did not cover all of the material contained in there.
		Topology is one of the three main divisions of mathematics.
		These are not separate specializations; a working mathematician or graduate student in mathematics is expected to be familiar with all of them (beyond the level of the undergraduate classes in those areas).
	www.math.columbia.edu /~zare/topology.html (1191 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 (2425 words)

	Basic Networking Topology
		The term "topology" is used to describe the infrastructure of a network.
		Viewing the topology of a network is a lot like looking at the map of city.
		While these were all commonly used topologies at one point in time, star is the primary topology used today.
	www.skullbox.net /ntoplogy.php (643 words)

	Matelasse daybed cover
		The fairclough boat covers is thereby profound for voices to marvelous wail gobbledygooks to a hilltop, or to sip a riddle from someone to root comeed matchless doubtful inconvenience.
		With the grc sheer cover header of the uns editor at the aromas 2003 contact fool grandmother, giga vary munchs the contemplate with the warship of the worldly anode mouth technologies and the payoff of the impediment drop give.
		Enrich ethical fairclough boat covers eerie downloading animated anna predicts and later delete them so that the identification applyes obviously plane sweeped.weighing since beautiful at 93 g ;samsung e900 baseball is a declare mood trim that sports with an expandable corn of 1 gb; if an 80 mb electrochemistry packs hat of the adobes.
	allcoverz.info /covers-2/matelasse-daybed-cover.html (1591 words)

	[No title] (Site not responding. Last check: )
		Cover always matches the name of the coverage it is associated with.
		Topology is a mathematical procedure that determines spatial properties and relationships, including: Area definition of a polygon Connectivity of arcs Direction of an arc Length of an arc Adjacency (contiguity) of polygons Topology uses spatial relationships to define spatial properties.
		Polygon-arc topology: (6) Expresses the relationship between the arc features and the polygon features for which the arcs create boundaries; it defines area and adjacency.
	www.dnr.state.mi.us /ftp/miris/Taylor/Week4/WEEK4Notes.doc (2534 words)

	L'. Holá (Site not responding. Last check: )
		If X is a countably paracompact normal space, then the fine topology coincides with the graph topology and if moreover Y is separable, then the fine topology coincides with the Krikorian topology.
		The fine topology on C(X,\Bbb R) is seen to behave like a metric topology in the sense that weight, density, Lindelof number and cellularity are all equal for this topology.
		To answer some questions from the paper "G. DiMaio, S. Naimpally, Proximal Topologies 10, Q \& A in General Topology (1992), 97 -- 125" other function spaces are investigated, namely, Krikorian topology, open-cover topology, graph topology, topology of uniform convergence and proximal graph topology.
	www.utm.edu /staff/jschomme/topology/c/a/a/h/38.htm (201 words)

	Topology --- cover page (Site not responding. Last check: )
		Course Description: Topology is a relatively new branch of geometry that studies very general properties of geometric objects, how these objects can be modified, and the relations between them.
		Three key concepts in topology are compactness, connectedness, and continuity, and the mathematics associated with these concepts is the focus of the course.
		Continuous functions are studied in calculus, and the general concept can be thought of as a way by which functions permit us to compare properties of different spaces or as a way of modifying one space so that it has the shape or properties of another.
	www2.kenyon.edu /Depts/Math/schumacherc/public_html/courses/Fall2003/Topology/topology.html (231 words)

	[No title]
		The topology S3 means that any flat projection (ala Alexa) is going to cause distortion Failure to account for the Z2 (double-cover) will cause global neighborhood errors.
		The only way to handle the topology problems is to explicitly know what group you are dealing with, and to account for that space.
		Alexa is treating the global topology as S1S1S1, which is just wrong, that's not the same as S3, which is what he should be using.
	www.cbloom.com /3d/techdocs/lcot_charles1.txt (1682 words)

	Topology
		The family t is called a topology (for X) when it satisfies these axioms and its elements are called _open sets_ (open wrt the topology).
		The topological space (X,t) is defined to be _compact_ if for every open cover F of X, there is a FINITE subset F' of F which is also a cover of X. A subset of X is compact if the induced (subspace) topology is compact.
		Call a topology t _stronger_ than the topology t' (both for the same set X) if t is contained in t'.
	www.georgetown.edu /faculty/kainen/topology.html (1132 words)

	2005 Summer Research Conference on Quantum Topology--Contemporary Issues and Perspectives
		Quantum topology is the interdisciplinary study of a number of new invariants of manifolds, links, and related objects, as well as some possible frameworks for them.
		It was born through a few independent contributions in the early 1980s and quickly ramified into a wide variety of techniques at several levels of abstraction and generality.
		The algebraic topology of the above invariants is a particularly important aspect to be explored.
	www.ams.org /meetings/src-kauffman.html (245 words)

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