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Topic: Directed set

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Total order

Net (topology)

Preorder

Equivalence relation

Limit (category theory)

Limit (mathematics)

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	Directed set - Wikipedia, the free encyclopedia
		Directed sets are generalizations of totally ordered sets.
		Directed sets need not be antisymmetric and therefore in general are not partial orders.
		Directed subsets are most commonly used in domain theory, where one studies orders for which these sets are required to have a least upper bound.
	en.wikipedia.org /wiki/Directed_set (486 words)

	Directed set -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Directed sets in this form are used to define (An open fabric of string or rope or wire woven together at regular intervals) nets in (The configuration of a communication network) topology.
		The set of (The number 1 and any other number obtained by adding 1 to it repeatedly) natural numbers N with the ordinary order ≤ is a directed set (and so is every (Click link for more info and facts about totally ordered set) totally ordered set).
		Directed subsets are most commonly used in (Click link for more info and facts about domain theory) domain theory, where one studies orders for which these sets are required to have a (Click link for more info and facts about least upper bound) least upper bound.
	www.absoluteastronomy.com /encyclopedia/d/di/directed_set.htm (650 words)

	Compact element - Wikipedia, the free encyclopedia
		In the mathematical area of order theory, the compact or finite elements of a partially ordered set are those elements that cannot be subsumed by a supremum of any directed set that does not already contain members above the compact element.
		For the case of the join-semilattices note that any set can be turned into a directed set with the same supremum by closing under finite (non-empty) suprema.
		When considering directed complete partial orders or complete lattices the additional requirements that the specified suprema exist can of course be dropped.
	en.wikipedia.org /wiki/Compact_element (545 words)

	Domain theory - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		Indeed, in the theory of metric spaces, sequences play a role that is in many aspects analogue to the role of directed sets in domain theory.
		The notation is nonetheless motivated by certain parallels to the respective notions in set theory and topology.
		The compact elements of a domain have the important special property that they cannot be obtained as a limit of a directed set in which they did not already occur.
	open-encyclopedia.com /Domain_theory (2500 words)

	Graph (mathematics) - Wikipedia, the free encyclopedia
		V (and hence E) are usually taken to be finite sets, and many of the well-known results are not true (or are rather different) for infinite graphs because many of the arguments fail in the infinite case.
		A distinction between a directed graph and an oriented simple graph is that if x and y are vertices, a directed graph allows both (x, y) and (y, x) as edges, while only one is permitted in an oriented graph.
		A quiver is sometimes said to be simply a directed graph, but in practice it is a directed graph with vector spaces attached to the vertices and linear transformations attached to the arcs.
	en.wikipedia.org /wiki/Directed_graph (1370 words)

	Partially ordered set (Site not responding. Last check: 2007-11-07)
		A partial order is a binary relation R over a set P which is reflexive, antisymmetric, and transitive, i.e., for all a, b and c in P, we have that:
		In particular, totally ordered sets can also be referred to as "ordered sets", especially in areas where these structures are more common than posets.
		Strict partial orders are also useful because they correspond more directly to directed acyclic graphs (dags): every strict partial order is a dag, and the transitive closure of a dag is both a strict partial order and also a dag itself.
	stevehome.dynup.net /en/Ordered_set.htm (424 words)

	Whats Graph Theory
		Though the set of vertices is the same (the set of blocks), the set of the edges is different.
		If the directed graph in question is weighted (there is a numerical value associated with each vertex) then the maximum closure is the closure with the greatest value obtained by summing all the weights in the closure.
		The graph whose directed edges indicate "block Y is in the overburden of a block X" is therefore the transitive closure of the slope graph.
	www3.telus.net /public/nstuart/pan/grtheory.htm (3426 words)

	several replies re: chains vs. directed sets
		Directed completeness is a more mathematically elegant condition; it is particularly useful when one is working with compact elements.
		The isolated (aka finite, compact, basic) elements which approximate x form a directed set, but not generally a chain.
		Plotkin in his `Pisa Notes' indicated that for omega-algebraic cpos chains and directed sets are interchangeable.
	www.seas.upenn.edu /~sweirich/types/archive/1991/msg00104.html (339 words)

	Wlodek M Zuberek: TPN-tools -- introduction
		The set of all possible marking functions which can be derived in such a way is called the set of reachable markings (or the forward marking class) of a net.
		The original set of places is partitioned into a set of disjoint classes, and each class is replaced by a single place with token colors indicating which of the original places the tokens belong to.
		Similarly, the original set of transitions is partitioned into a set of disjoint classes, and each class is replaced by a single transition with occurrences indicating which of the original transitions the firing corresponds to.
	www.cs.mun.ca /~wlodek/tpntools/tpntools-intro.html (1349 words)

	Graphs
		For example, a directed graph may be acyclic but its undirected equivalent is usually not.
		However, this is not the set of edges in the subgraph that is spawned by
		For example, a two pass algorithm might move a node in x direction in the first pass, and in y direction in the second pass.
	www.infosun.fmi.uni-passau.de /Graphlet/graphscript/graphs.html (1722 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		A directed graph is composed of two sets: the node set and the edge set.
		The elements of the node set are instances of Nodes.
		The node set is // unaltered public void removeEdge(Node n1, Node n2) { // Find the relevant sub-vector in the edges vector using the // position of n1 in the nodes vector, then remove n2 from that // sub-vector.
	www.cs.toronto.edu /~reiter/a3Part2Fall99 (1537 words)

	Glossary of order theory (Site not responding. Last check: 2007-11-07)
		An ideal is a subset X of a poset P that is a directed lower set.
		Equivalently, a set is a prime filter iff its complement is a prime ideal.
		For a poset P and a subset X of P, the least element in the set of upper bounds of X (if it exists, which it may not) is called the supremum, join, or least upper bound of X.
	www.free-download-soft.com /info/startup-manager.html (2564 words)

	chains, etc & announcement on intuitionistic Tarski theorem
		Now, given a countable (ie enumerated) directed set, we can choose an increasing sequence in it which is cofinal.
		The result can be proved by induction on cardinals: assuming that the given directed set actually has bounds within itself not just of pairs but of sets smaller than the cardinal under consideration, we can choose a transfinite increasing cofinal sequence.
		By considering the smallest set closed under arbitrary joins and application of the function, it is not difficult to prove Tarksi's theorem for complete lattices intuitionistically.
	www.cis.upenn.edu /~bcpierce/types/archives/1991/msg00111.html (725 words)

	Study of Exceptional Talent (SET)
		Since 1980, SET has assisted students throughout the U.S. who exhibit extraordinary mathematical or verbal reasoning ability by scoring at least 700 on either the mathematical or verbal part of the SAT I before the age of 13.
		SET also hosts a listserv and a mentor program to enable SET members to connect with and advise one another.
		SET's senior staff also offers educational and career counseling to students not involved in SET through CTY's Diagnostic and Counseling Center.
	www.cty.jhu.edu /set (429 words)

	Kids.net.au - Encyclopedia Directed set - (Site not responding. Last check: 2007-11-07)
		In mathematics, a directed set is a set A together with a binary relation <= having the following properties:
		Nets generalize sequences and unite the various notions of limit.
		Note that directed sets need not be antisymmetric and therefore in general are not partial orders.
	www.kids.net.au /encyclopedia-wiki/di/Directed_set (227 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		A set of (directed) edges H (a subset of E) is a Hamiltonian cycle of G, if it is a cycle and goes through each vertex of G exactly once.
		INPUT: An directed graph given by the set of ground atoms "vtx(v)", v=1,2,...,n, where n is the number of vertices, and "edge(x,y)" for each directed edge (x,y).
		In each case, the vertex set is {1,2,...,200}, the edge set has 1250 elements; only the edges are listed in the data sets given below.
	www.cs.engr.uky.edu /ai/benchmark-suite/hamiltonian-cycle.html (104 words)

	AntiOffline We really DO give a flying f##k (Site not responding. Last check: 2007-11-07)
		Some of the commands were gathered around the net others I have implemented and tested along the way in the midst of attacks as well as in labs.
		If this is set to 1 and ip_forwarding is set to 0, then # a packet sent to an interface from which it did not arrive will be # dropped.
		This setting prevents an attacker from passing packets across # a machine with multiple interfaces that is not acting a router.
	www.antioffline.com /stoppingdos.html (2331 words)

	PlanetMath: net (Site not responding. Last check: 2007-11-07)
		A net is a map from a directed set to X. In other words, it is a pair
		Cross-references: convergent, compact, continuous at, subspace, Hausdorff, sequences, cofinal, accumulation point, neighbourhood, open, iff, converge, topological space, directed set, map
		Hi, I am new to this forum and am not in particular very good in set theory, but I could not quite comprehend the claim made in the first paragraph of the definition for "net", that xA<=aB iff A<=B. Doesnt the mapping have to be monotonous for that claim to be valid?
	planetmath.org /encyclopedia/Net.html (157 words)

	order 20.nb
		We can also define a partial order where given any two sets there is always a smaller set (or one that precedes the two elements).
		A lattice is a directed set in both directions.
		It is interesting to note that, generally speaking, a directed set need not be a lattice.
	www.sas.org /E-Bulletin/2003-03-21/mathCorner/body.html (244 words)

	DigraphPaper.nb
		The first indgredient for a digraph IFS is a directed multi-graph which describes the combinatorics of how the pieces fit together.
		However, we may characterize its largest scaling factor by the spectral radius of the linear part, which is the maximum of the absolute values of all its complex eigenvalues.
		Such a collection of sets is called the invariant list of the digraph IFS and we will refer to its members as digraph fractals.
	www.unca.edu /~mcmcclur/professional/DigraphFractals/Links/index_lnk_2.html (308 words)

	PlanetMath: directed set (Site not responding. Last check: 2007-11-07)
		A directed set is a partially ordered set
		Cross-references: property, antisymmetric, iff, residual, subset, partially ordered set
		This is version 3 of directed set, born on 2002-08-01, modified 2003-02-08.
	planetmath.org /encyclopedia/DirectedSet.html (65 words)

	Directed set (Site not responding. Last check: 2007-11-07)
		In mathematics, a directed set is a set A together with a binary relation ≤ having the following properties:
		Directed sets in this form are used to define nets in topology.
		Nets generalize sequences and unite the various notions of limit used in analysis.
	www.sciencedaily.com /encyclopedia/directed_set (410 words)

	General Topology - NoiseFactory Science Archives (http://noisefactory.co.uk)
		Closed subsets of compact sets are themselves compact, and conversely any compact subspace of a Hausdorff space is closed.
		We will be given a set of functions from a common domain onto a selection of image spaces, and have to create the appropriate topology for the domain.
		The finite sets themselves are directed under set inclusion, because two finite sets are bounded above by their union, which is also finite.
	noisefactory.co.uk /maths/topology.html (4788 words)

	ONLINE - International News Network
		He also directed that filtration plants should be set up in Sargodha, Ziarat, Hydrabad and Mardan on priority basis due to deteriorating water quality in these areas.
		Prime Minister also directed to set up low cost crip and sprinkler system of irrigation and desalination units for purification of water in coastal areas of the country.
		He maintained that provincial and district governments should also make efforts with collaboration with industrialists to set up industrial affluent treatment plants besides urging the need to ensure a safe sewerage system that underground water was not contaminated and use of chlorination method to provide safe nad healthy water to people.
	www.onlinenews.com.pk /details.php?id=72755 (380 words)

	\bf The Duality Between Aglebraic Posets and Bialgebraic Frames: A Lattice Theoretic Perspective
		The sets associated with the stages of the process are to represent refinements in the approximations of the desired result.
		The previous result, although a direct consequence of Theorem 4.11 and the well-known results of this section, does not seem to appear in the literature concerning algebraic posets.
		It is a direct consequence of Lemmas 4.1 and 5.7.
	www.mtsu.edu /~jhart/ALGFRM.html (9751 words)

	directed
		Nearby terms: Direct Client to Client Protocol « Direct Connection « directed acyclic graph « directed graph » Directed Oc » directed set » Direct Inward Dialing
		Directed Oc language> (Doc) A language related to Oc.
		Nearby terms: Direct Connection « directed acyclic graph « directed graph « Directed Oc » directed set » Direct Inward Dialing » directional coupler
	www.linuxguruz.com /foldoc/foldoc.php?directed (209 words)

	PlanetMath: (Site not responding. Last check: 2007-11-07)
		difference between sets (=set difference) owned by yark
		direct sum (=categorical direct sum) owned by djao
		direct sum of even/odd functions (example) owned by mathcam
	planetmath.org /encyclopedia/D (1478 words)

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