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Topic: Separated sets

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	Separated sets - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certain way.
		The notion of when two sets are separated or not is important both to the notion of connected spaces (and their connected components) as well as to the separation axioms for topological spaces.
		Separated sets should not be confused with separated spaces (defined below), which are somewhat related but aren't the same thing.
	en.wikipedia.org /wiki/Separated_sets (985 words)

	Separation axiom - Wikipedia, the free encyclopedia
		The separation axioms are about the use of topological means to distinguish disjoint sets and distinct points.
		The separation axioms all say, in one way or another, that points or sets that are distinguishable or separated in some weak sense must also be separated in some stronger sense.
		There are several stronger forms of separatedness for sets; they are in order: separated by neighbourhoods; separated by closed neighbourhoods, separated by a function, and separated precisely by a function.
	en.wikipedia.org /wiki/Separation_axiom (1489 words)

	A Helly-type theorem for hyperplane transversals to well-separated convex sets - Aronov, Goodman, Pollack, Wenger ...
		A Helly-type theorem for hyperplane transversals to well-separated convex sets - Aronov, Goodman, Pollack, Wenger (ResearchIndex)
		A Helly-type theorem for hyperplane transversals to well-separated convex sets (2001)
		A Helly-type theorem for hyperplane transversals to well-separated convex sets.
	citeseer.ist.psu.edu /408007.html (484 words)

	Separated sets -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Separated sets should not be confused with (Click link for more info and facts about separated space) separated spaces (defined below), which are somewhat related but aren't the same thing.
		A and B are separated by neighbourhoods if there are a (People living near one another) neighbourhood U of A and a neighbourhood V of B such that U and V are disjoint.
		A and B are separated by closed neighbourhoods if there are a (Click link for more info and facts about closed) closed neighbourhood U of A and a closed neighbourhood V of B such that U and V are disjoint.
	www.absoluteastronomy.com /encyclopedia/S/Se/Separated_sets.htm (1223 words)

	Separated sets -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		The notion of when two sets are separated or not is important both to the notion of (Click link for more info and facts about connected space) connected spaces (and their connected components) as well as to the (Click link for more info and facts about separation axiom) separation axioms for topological spaces.
		This property has nothing to do with topology as such, but only (The branch of pure mathematics that deals with the nature and relations of sets) set theory; we include it here because it is the weakest in the sequence of different notions.
		Conversely, if a nonempty subset A is separated from its own complement, and if the only (A set whose members are members of another set; a set contained within another set) subset of A to share this property is the empty set, then A is an open-connected component of X.
	www.absoluteastronomy.com /encyclopedia/s/se/separated_sets.htm (1223 words)

	Topology glossary : Contractible (Site not responding. Last check: 2007-11-07)
		The boundary of a set is the set's closure minus its interior.
		A dense set is a set whose closure is the whole space.
		Two sets A and B in a space are functionally separated if there is a continuous function from the space into the interval [0,1] with the property that A is mapped to 0 and B is mapped to 1.
	www.termsdefined.net /co/contractible.html (1170 words)

	PlanetMath: separated (Site not responding. Last check: 2007-11-07)
		In [2], separated sets are called strongly disjoint sets.
		Cross-references: closed set, clopen set, open balls, intervals, homeomorphism, topological space, subsets
		This is version 7 of separated, born on 2005-05-17, modified 2005-05-20.
	planetmath.org /encyclopedia/Separated.html (72 words)

	Method and device for simultaneous screening of sets of color-separated half-tone negatives - Patent 4027969 (Site not responding. Last check: 2007-11-07)
		Apparatus for simultaneous screening of sets of color-separated half-tone negatives, two or more registering images of the negatives can be projected simultaneously on photographic film by adjusting the configuration of the film support to counteract the distortion caused by the reproduction lens.
		In order to secure the engagement of all screws 8 with the upper side of plate 7 there is drilled in plate 6 near each hole 9 a hole 10 for a clamping screw 11 engaging with its head an enlarged upper portion of the hole 10.
		By different setting of the screws 8 and 11 such deformation and surface configuration of the resilient plate 6 is possible to obtain, that the optical distorsion of the projected images is counteracted, and good registration of the images will be obtained.
	www.freepatentsonline.com /4027969.html (1500 words)

	Separated Shoulder (Site not responding. Last check: 2007-11-07)
		In topology and related branches of mathematics, separated sets are pairs of subsets of a given topological space that are related to each other in a certainway.
		A and B are separated in X if each is disjoint from theother's closure.
		The closures themselves don't have to bedisjoint from each other; for example, the intervals [0,1) and (1,2] are separated in the realline R, even though the point 1 belongs to both of their closures.
	www.witchware.com /File/31409-Separated.Shoulder.Html (669 words)

	[No title]
		Ted Votteler successfully separated 3-week-old ischiopagus (joined at the lower trunk and pelvis) twins at Children's Medical Center Dallas.
		In all of its separation surgeries, at least one twin survived.
		Ahmed and Mohamed Ibrahim are the first set of craniopagus (joined at the head) twins that neurosurgeons on the medical staff at Children's Medical Center Dallas will attempt to separate.
	www.childrens.com /twins/history.cfm (573 words)

	[No title]
		] Sets A and B in a topological space are separated if both the closure of A intersected with B and the closure of B intersected with A are disjoint.
		] The separation of liquids or gases in a mixture, as by distillation or extraction.
		A machine for separating materials of different specific gravity by means of water or air.
	www.accessscience.com /Dictionary/S/S17/DictS17.html (2741 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Note that any two separated sets must be disjoint.
		Note that we sometimes use the terminology of separated sets to refer to points; in that situation, we're really talking about the singleton set {x} rather than the point x.
		In fact, in a normal space, any two disjoint sets will also be separated by a function; this is Urysohn's Lemma.
	www.online-encyclopedia.info /encyclopedia/s/se/separation_axiom.html (1450 words)

	Where are city's 1st successfully separated (Site not responding. Last check: 2007-11-07)
		The twins were successfully separated in a six-hour procedure during the neonatal period but succumbed to kidney failure on the fourth and fifth days respectively.
		Conjoined twins are developed when the embryo, which is separating into identical twins, stops mid-way, leaving the partially separated egg to grow into a conjoined foetus.
		Separating the brain material and circulatory system that the boys shared was their most challenging task.
	web.mid-day.com /news/city/2003/october/66446.htm (719 words)

	PlanetMath: separation axioms (Site not responding. Last check: 2007-11-07)
		The separation axioms are additional conditions which may be required to a topological space in order to ensure that some particular types of sets can be separated by open sets, thus avoiding certain pathological cases.
		point and a compact set in a Hausdorff space have disjoint open neighborhoods.
		This is version 19 of separation axioms, born on 2003-02-23, modified 2005-07-02.
	planetmath.org /encyclopedia/SeparationAxioms.html (502 words)

	News-Star OnlineTwo sets of twins separated in Oklahoma 07/11/03
		Oklahoma surgeons have separated two sets of conjoined twins, one in 1970 and the other in 1986.
		Pryor teenagers Faith and Hope Cox, born joined at the abdomen, were separated by a surgical team from The Children's Hospital at OU Medical Center on Christmas Eve 1986.
		Charles and Natalie Cox knew their daughters were conjoined before birth and were hopeful of a successful separation when the girls were born Dec. 23.
	www.news-star.com /stories/071103/New_24.shtml (555 words)

	Connectedness (Site not responding. Last check: 2007-11-07)
		X cannot be divided into two disjoint nonempty closed sets (This follows since the complement of an open set is closed).
		The only sets which are both open and closed (clopen sets) are X and the empty set.
		X cannot be written as the union of two nonempty separated sets.
	www.freecaviar.com /search.php?title=Connectedness (720 words)

	Corpus Christi Caller Times Caller.com - Siamese twins separated after 8-hour surgery
		The girls, born June 4 in a hut in an African village, had separate vital organs, but the bases of their spines were fused.
		The bone had to be separated, and surgeons had to fashion new anal openings for both.
		The hospital successfully separated sets of Siamese twins in 1978 and 1980.
	www.oldconcretestreet.com /2000/september/13/today/national/4186.html (344 words)

	Causes (Site not responding. Last check: 2007-11-07)
		It is estimated that 70 percent of conjoined twins are female.
		If possible, delay of separation procedures is wise in order to allow for growth and development that will increase chances of survival.
		He said the operation at the private Policlinico Agostino Gemelli in Rome was perhaps less complex than surgery that began in Dallas on Saturday to divide the circulatory systems of two-year-old Egyptian twins joined at the crown of their heads.
	www.angelfire.com /tx3/rebeccaoz/causes/ConjoinedTwins.html (1113 words)

	CAUSALITY - Discussion
		We start by considering separation between two singleton variables, x and y; the extension to sets of variables is straightforward (i.e., two sets are separated if and only if each element in one set is separated from every element in the other).
		Motivation: When we measure a set Z of variables, and take their values as given, the conditional distribution of the remaining variables changes character; some dependent variables become independent, and some independent variables become dependent.
		Rule 2: x and y are d-connected, conditioned on a set Z of nodes, if there is a collider-tree path between x and y that traverses no member of Z.
	bayes.cs.ucla.edu /BOOK-2K/d-sep.html (944 words)

	Pediatric Neurosurgeon Benjamin Carson, M.D. to Separate Adult Conjoined Twins in Singapore
		Carson, whose experience includes the first separations of twins joined at the back of the head and of twins joined at the tops of the head, will lend his expertise to the Singapore team in a consulting role.
		In general, the risks during and after separation include anesthesia and surgical complications.
		Carson says the age of the twins presents additional risks, both because their adult brains have lost a great deal of the plasticity that may be needed to reorganize functional areas and because the psychological impact is likely to be greater than in children.
	www.hopkinsmedicine.org /press/2003/June/030612.htm (759 words)

	State Recommended IEP Forms and Instructions
		Forms are separated into the sets required for an initial or triennial meeting and sets required for an annual review.
		Forms are further separated into sets to be used for Early Childhood, for students in kindergarten through age 13, and for students age 14 and older.
		Be sure to check with the special education director in your Administrative Unit to learn whether the Administrative Unit requires the use of IEP forms that are different from the State recommended IEP forms.
	www.cde.state.co.us /cdechart/guidebook/sped/iep.htm (194 words)

	Articles - Weight training (Site not responding. Last check: 2007-11-07)
		Sets of 1 to 5 repetitions primarily develop strength, with less impact on muscle size and none on endurance.
		Sets of more than 20 repetitions are considered to be an aerobic exercise.
		The cardiovascular effort to recover from each set serves a function similar to an aerobic exercise, but this not the same as saying that a weight training set is itself an aerobic process.
	www.pilates-move.com /articles/Weight_training (4485 words)

	[No title]
		Thus all the red points (set A) have positive x coordinates, and hence their dual lines have positive slopes, whereas all the blue points (set B) have negative x coordinates, and hence their dual lines have negative slopes.
		Unlike most of the structures we have seen up to now, a line arrangement is not defined in terms of a set of points, but rather in terms of a set L of lines.
		Given an arrangement A of a set L of n lines, and given a line l that is not in L, the zone of l in A(l), denoted ZA (l), is the set of faces whose closure intersects l.
	www.cs.wustl.edu /~pless/506/l20.html (2826 words)

	[No title]
		There are four possible sets of axes available; the keyword is used to select the axes for which a particular line should be scaled.
		In all cases, the numbers on each record of a data file must be separated by white space (one or more blanks or tabs), unless a format specifier is provided by the `using` option.
		Data separated by double blank records are treated as if they were in separate data files.
	www.people.virginia.edu /~lz2n/mse524/Eduardo/gnuplot-help.txt (1073 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		The qy parameter associates a root node set with a query.
		The nsroot parameter associates a non-root node with its root node set.
		A node set cannot be associated with a query and a root node set at the same time.
	iw.stanford.edu /iwregistrar/CreateNodeSet (202 words)

	Iranian twins separated, surgery to last for another 24 hours
		Neurosurgeons on Tuesday finished separating two 29-year-old Iranian twins joined at the head, who were in critical condition, a hospital spokesman said.
		The brains of Ladan and Laleh Bijani were separate, but after lying alongside each other for decades were nonetheless stuck together, a Raffles Hospital spokesman said.
		This is the first time surgeons have tried to separate adult craniopagus twins - siblings born joined at the head.
	www.chinadaily.com.cn /en/doc/2003-07/08/content_243915.htm (927 words)

	Solutions to Problem set 5
		Let us show that the union of two connected sets with non-empty intersection is connected.
		The interior is the union of the two open quadrants and these are separated, since the closure of each is the corresponding closed quadrant so the union is not connected.
		Remark: Note that separable and separated are rather unrelated concepts.
	www-math.mit.edu /~rbm/18.100-S04/node7.html (499 words)

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