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Topic: Long line topology

	Long line (topology) - Wikipedia, the free encyclopedia
		It makes sense to consider all the long spaces at once, however, because every connected (non-empty) one-dimensional (not necessarily separable) topological manifold possibly with boundary, is homeomorphic to either the circle, the closed interval, the open interval (real line), the half-open interval, the closed long ray, the open long ray, or the long line.
		The long line or ray can be equipped with the structure of a (non-separable) differentiable manifold (with boundary in the case of the closed ray).
		The long line or ray can even be equipped with the structure of a (real) analytic manifold (with boundary in the case of the closed ray).
	en.wikipedia.org /wiki/Long_line_%28topology%29 (941 words)

	Lower limit topology - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-31)
		In mathematics, the lower limit topology or right half-open interval topology is a topology defined on the set R of real numbers; it is different from the standard topology on R and has a number of interesting properties.
		It is the topology generated by the basis of all half-open intervals [a,b), where a and b are real numbers.
		The lower limit topology is finer (has more open sets) than the standard topology on the real numbers (which is generated by the open intervals).
	www.sciencedaily.com /encyclopedia/lower_limit_topology (323 words)

	Line
		The word line derives from the Latin lingui, meaning flax plant from which linen is produced; at one time, a stretched linen thread was the most reliable way to determine a straight line.
		In sewing and tailoring, a line or ligne is the unit of measure for sizing buttons, with 40 lines to the inch.
		A line may also be a dose of cocaine or amphetamine arranged in a line ready to be snorted.
	www.brainyencyclopedia.com /encyclopedia/l/li/line.html (401 words)

	Long line (topology) (Site not responding. Last check: 2007-10-31)
		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.
		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, Operads and Quantisation A workshop of the EPSRC Symposium on Geometry and Topology.
	www.serebella.com /encyclopedia/article-Long_line_(topology).html (1247 words)

	Line segment - Wikipedia, the free encyclopedia
		In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points.
		More generally, when the end points are both vertices of a polygon, the line segment is either an edge (of that polygon) if they are adjacent vertices, or otherwise a diagonal.
		When the end points both lie on a curve such as a circle, a line segment is called a chord (of that curve).
	en.wikipedia.org /wiki/Line_segment (250 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.
		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.
		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".
	www.math.niu.edu /~rusin/known-math/index/54-XX.html (2431 words)

	Learn more about Line in the online encyclopedia. (Site not responding. Last check: 2007-10-31)
		The word line apparently derives from the Latin linum, meaning flax plant from which linen is produced; at one time, a stretched linen thread was the most reliable way to determine a straight line.
		More abstractly, one usually thinks of the real line as the prototype of a line, and assumes that the points on a line stand in a one-to-one correspondence with the real numbers.
		The "straightness" of a line, interpreted as the property that it minimizes distances between its points, can be generalized and leads to the concept of geodesics on differentiable manifolds.
	www.onlineencyclopedia.org /l/li/line.html (495 words)

	Long line topology - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-31)
		Start the Long line topology article or add a request for it.
		Look for "Long line topology" in the Wikimedia Commons, our repository for free images, music, sound, and video.
		Promotional articles about yourself, your friends, your company or products; or articles written as part of a marketing or promotional campaign, may be deleted in accordance with our deletion policies.
	www.sciencedaily.com /encyclopedia/long_line__topology_ (188 words)

	Long line (topology) (Site not responding. Last check: 2007-10-31)
		A related space the extended long line L * is obtained by adjoining an additional to the end of L.
		The extended long line L * is compact ; it is the one-point compactification of L.
		It is also connected but not path-connected because the long line is 'too to be covered by a path which an image of an interval.
	www.freeglossary.com /Long_line_%28topology%29 (650 words)

	Long-line fishing - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-31)
		See also long line (topology) and long line (telecommunications).
		Long-line fishing is a commercial fishing technique that uses hundreds or even thousands of baited hooks hanging from a single line.
		Swordfish, tuna and Patagonian toothfish are commonly caught by this method.
	www.encyclopedia-online.info /Long-line_fishing (67 words)

	Science Fair Projects - Connected space
		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.
		Example of connected spaces that are not path-connected include the extended long line L* and the topologist's sine curve.
		However, subsets of the real line R are connected if and only if they are path-connected; these subsets are the intervals of R.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Connectedness (886 words)

	Long line (topology) (Site not responding. Last check: 2007-10-31)
		Arelated space, the extended long line, L*, is obtained by adjoining an additional element to the end ofL.
		The extended long line L* is compact ; it is the one-point compactification of L.
		It is also connected, but not path-connected becausethe long line is 'too long' to be covered by a path, which is an image of an interval.
	www.therfcc.org /long-line-topology--3913.html (268 words)

	Order topology (Site not responding. Last check: 2007-10-31)
		The same argument as before shows that the subspace topology on Z is not equal to the induced order topology on Z, but one can show that the subspace topology on Z cannot be equal to any order topology on Z. An argument follows.
		The left order topology is the standard topology used for many set-theoretic purposes on a Boolean algebra.
		Topology and combinatorics: hyperplane arrangements, the topology and geometry of manifolds, the homology of discrete groups, the homotopy theory of high-dimensional knots.
	www.omniknow.com /common/wiki.php?in=en&term=Order_topology (2272 words)

	PlanetMath: examples of locally compact and not locally compact spaces
		The Long Line is a locally compact topological space.
		If you take any unbounded totally ordered set and equip it with the left order topology (or right order topology), you get a locally compact space.
		This is version 14 of examples of locally compact and not locally compact spaces, born on 2002-06-23, modified 2006-04-24.
	www.planetmath.org /encyclopedia/ExamplesOfLocallyCompactAndNotLocallyCompactSpaces.html (329 words)

	Definition of index.php?search=line&limit=20&offset=120 (Site not responding. Last check: 2007-10-31)
		The line was defended by XIV Panzer Corps.
		When the lines are close together the gradient is large: the va...
		As such, the ''line element'' is then naturally a function of the met...
	www.wordiq.com /knowledge/index.php?search=line&limit=20&offset=120 (755 words)

	Upper limit topology (Site not responding. Last check: 2007-10-31)
		In mathematics, the lower limit topology or righthalf-open interval topology is a topology defined on theset R of real numbers ; it is different from the standardtopology on R and has a number of interesting properties.
		and called the Sorgenfrey line after Robert Sorgenfrey, often servesas a useful counterexample in general topology, like the Cantor set and the long line.
		The lower limit topology is finer (has more open sets) than thestandard topology on the real numbers (which is generated by the open intervals).
	www.therfcc.org /upper-limit-topology-219164.html (248 words)

	NationMaster - Encyclopedia: Ll (Site not responding. Last check: 2007-10-31)
		Long lines, a term for a long-distance telephone network
		See: long line (topology) long line (telecommunications) long-line fishing This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title.
		The telephone or phone (Greek: tele = far away and phone = voice) is a telecommunications device which is used to transmit and receive sound (most commonly voice and speech) across distance.
	www.nationmaster.com /encyclopedia/Ll (765 words)

	AnglerBait Fishing Long Line
		Get $20 per month best long distance fishing line and make unlimited long distance calls to anywhere in the US, cheap best long distance fishing line with SBC.
		A long line fishing quickly sells a preparation by the use of.
		The average long line fishing shapes, after that some safe route plays.
	www.anglerbait.com /10/fishing-long-line.html (300 words)

	Long Line Fishing
		Manufacturers of commercial long line fishing reels, associated equipment and gear for tuna and swordfish fishing.
		Long line fishing could pose threats to these unique and...
		The aggresive fishing of sharks with the long line method, threatens the population of sharks in the Galapagos Marine Reserve.
	www.fishing-fish.com /fish/long-line-fishing.html (476 words)

	Connected space (Site not responding. Last check: 2007-10-31)
		In topology and related branches of mathematics, a topological space is said to be connected if it cannot be divided into two disjoint nonempty open set s whose union is the entire space.
		Equivalently, it can't be divided into two disjoint nonempty closed set s (since the complement of an open set is closed).
		The space X is said to be path-connected if for any two points x and y in X there exists a continuous function f from the unit interval [0,1] to X with f (0) = x and f (1) = y.
	www.serebella.com /encyclopedia/article-Connected_space.html (855 words)

	NationMaster - Encyclopedia: Dory (Site not responding. Last check: 2007-10-31)
		Two-masted fishing schooner A schooner is a type of sailing ship characterized by the use of fore-and-aft sails on two or more masts.
		More glamorously, dories were once used to travel dangerous whitewater rivers, where their superior maneuverability made them preferable over other watercraft available at the time.
		Rainbow trout (Oncorhynchus mykiss) Trout is the common name given to a number of species of freshwater fishes belonging to the salmon family, Salmonidae.
	www.nationmaster.com /encyclopedia/Dory (1238 words)

	PlanetMath: long line
		endowed with the order topology induced by the lexicographical order, that is the order defined by
		Some of the properties of the long line:
		This is version 12 of long line, born on 2003-02-27, modified 2006-06-23.
	www.planetmath.org /encyclopedia/LongLine.html (228 words)

	AnglerBait Fishing Long Line
		The Fishing Line, Long Islands official fishing voice.
		"The Fishing Line" is proud to be the official fishing link of the.
		This new fishing catamaran is to operate in the East Coast Tuna long line fishery..
	www.anglerbait.com /2/fishing-long-line.html (300 words)

	Lower limit topology (Site not responding. Last check: 2007-10-31)
		A course in topology by Sidney A. Morris in HTML with embedded GIFs.
		A workshop of the EPSRC Symposium on Geometry and Topology.
		The plastic limit is that moisture content of a soil at which it becomes too dry to be plastic, used together with the liquid limit to determine the plasticity index which when plotted against the liquid limit on the plasticity chart enables the classification of cohesive soils.
	www.omniknow.com /common/wiki.php?in=en&term=Half-open_interval_topology (1623 words)

	ipedia.com: Long line (telecommunications) Article (Site not responding. Last check: 2007-10-31)
		In telephone systems nomenclature a long line is a transmission line in a long-distance communications network such as carrier systems, microwave radio links,...
		In telephone systems nomenclature a long line is a transmission line in a long-distance communications network such as carrier systems, microwave radio links, geosynchronous satellite links, underground cables, aerial cables and open wire, and submarine cables.
		In the United States, some of this technology was spun-off into the corporate entity known as AT&T Long Distance with the breakup of AT&T;.
	www.ipedia.com /long_line__telecommunications_.html (127 words)

	David Gauld's home page
		This meeting was organised by Gaven Martin, Akio Kawauchi, Tsukasa Yashiro and me. The second had theme Geometric Methods in the Topology of 3-Dimensional Manifolds and was held in Taipa, a seaside resort in the north of the North Island, from 8 to 15 January, 2006.
		My research interests are in set theoretic topology, especially applications to non-metrisable manifolds, and topological properties of manifolds near the limit of metrisability.
		Up to isotopy homeomorphisms of powers of the long ray and line behave just like homeomorphisms which permute the axes (and possibly reverse directions in the case of the line).
	www.math.auckland.ac.nz /~gauld (2430 words)

	Counterexamples in Topology - TheBestLinks.com - Cantor set, Euclidean space, Finite, Hilbert space, ... (Site not responding. Last check: 2007-10-31)
		Counterexamples in Topology, Cantor set, Euclidean space, Finite, Hilbert space...
		Counterexamples in Topology is a book by topologists Lynn A. Steen and J.
		who, together with their graduate students, canvassed the field of topology for a wide grouping of topological counterexamples.
	www.thebestlinks.com /Counterexamples_in_Topology.html (195 words)

	Home Page of F.D. Tall
		F.D. Tall, Consistency results in topology, II: Forcing and large cardinals, (invited paper), 423-427 in The Encyclopedia of General Topology, Elsevier, New York, 2003.
		K.P. Hart and F.D. Tall, Consistency results in topology, I: Quotable principles, 419-422 in The Encyclopedia of General Topology, Elsevier, New York, 2003.
		and the long line by their topological elementary reflections, Israel J. Math., 127 (2002) 81-94.
	www.math.toronto.edu /tall (277 words)

	long line fishing (Site not responding. Last check: 2007-10-31)
		On Still Waters the Long Pole can be used when fishing a deep swim ie 8 metres deep, in this situation you would use a 9 m pole.
		Long Pole to Hand Fishing is mainly used on Rivers this is the area I'm going to concentrate on.
		Operators of long-line fishing boats use monofilament lines up to 30 miles long and carrying...
	www.packlitepro.com /15/long-line-fishing.html (702 words)

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