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Topic: Regular space

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	Tychonoff space - Wikipedia, the free encyclopedia
		X is a completely regular space iff, given any closed set F and any point x that does not belong to F, there is a continuous function f from X to the real line R such that f(x) is 0 and f(y) is 1 for every y in F.
		Tychonoff spaces are precisely those topological spaces which can be embedded in a compact Hausdorff space.
		It is characterised by the universal property that, given a continuous map f from X to any other compact Hausdorff space Y, there is a unique continuous map g from βX to Y that extends f in the sense that f is the composition of g and j.
	en.wikipedia.org /wiki/Tychonoff_space (600 words)

	Regular space - Wikipedia, the free encyclopedia
		X is a regular space iff, given any closed set F and any point x that does not belong to F, there exists a neighbourhood U of x and a neighbourhood V of F that are disjoint.
		(Hausdorffness); all are equivalent in the context of regular spaces.
		On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide counterexamples to conjectures, showing the boundaries of possible theorems.
	en.wikipedia.org /wiki/Regular_space (942 words)

	Regular article - Regular military militia reserve 101st Airborne Division Mathematical - What-Means.com (Site not responding. Last check: 2007-11-07)
		In the military, a regular unit is a military unit that is part of the regular forces (not militia or reserve).
		In graph theory, a regular graph is a graph such that the all the degrees of the vertices are equal.
		In topology, a regular space is one in which points are closed and any point can be separated from any closed set by open sets.
	www.what-means.com /encyclopedia/Regular (231 words)

	Regular space -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		Most topological spaces studied in (Click link for more info and facts about mathematical analysis) mathematical analysis are regular; in fact, they are usually (Click link for more info and facts about completely regular) completely regular, which is a stronger condition.
		Regular spaces should also be contrasted with (Click link for more info and facts about normal space) normal spaces.
		On the other hand, spaces that are regular but not completely regular, or preregular but not regular, are usually constructed only to provide (Refutation by example) counterexamples to conjectures, showing the boundaries of possible (An idea accepted as a demonstrable truth) theorems.
	www.absoluteastronomy.com /encyclopedia/r/re/regular_space.htm (1243 words)

	Regular space (Site not responding. Last check: 2007-11-07)
		X is a regular space iff, given any closed set F and any point x that does not belong to F, there are a neighbourhood U of x and a neighbourhood V of F that are disjoint.
		Taking the interiorss of these closed neighbourhoods, we see that the regular open sets form a base for the open sets of the regular space X.
		Suppose that A is a set in a topological space X and f is a continuous function from A to a regular space Y.
	www.sciencedaily.com /encyclopedia/regular_space (981 words)

	Encyclopedia article on Topological space [EncycloZine] (Site not responding. Last check: 2007-11-07)
		A linear graph is a topological space that generalises many of the geometric aspects of graphs with vertices and edges.
		A space is regular if whenever C is a closed set and p is a point not in C, then C and p have disjoint neighbourhoods.
		A space is completely regular if whenever C is a closed set and p is a point not in C, then C and {p} are functionally separated.
	encyclozine.com /Topological_space (2350 words)

	PlanetMath: regular space (Site not responding. Last check: 2007-11-07)
		Definition 1 A topological space is a regular space if it is both a
		See Also: separation axioms, T0 space, T2 space, T3 space, Hausdorff space not completely Hausdorff, T1 space
		This is version 8 of regular space, born on 2002-02-08, modified 2005-03-26.
	planetmath.org /encyclopedia/Regular3.html (133 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		However, it has had problems with reserving a regular space for its thrice-weekly meditations, and is seeking a permanent location for worship.
		Space problems have been on the rise for religious groups around campus, Streets said.
		"She told me the art space was primarily for art and any student asking for it that night for that purpose had precedent," he said.
	www.buddhistnews.tv /current/yale-lotus-160404.php (648 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		Regular functions on affine space n-space are thus exactly the same as polynomials over k in n variables.
		It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal
		Just as with the regular functions on affine space, the regular functions on V form a ring, which we denote by k[V].
	en-cyclopedia.com /wiki/Algebraic_geometry (1655 words)

	Character design standards - Space Characters
		The no-break space is the same as the word space character with the added functionality of providing a way to prevent two words from being separated by a line break.
		The no-break space is not the same character as the figure space.
		The majority of these characters are traditional typographic space values or characters that are related to other character's width criteria.
	www.microsoft.com /typography/developers/fdsspec/spaces.htm (894 words)

	Macromedia - ColdFusion LiveDocs : Regular expression syntax (Site not responding. Last check: 2007-11-07)
		The pattern within the square brackets of a regular expression defines a character set that is used to match a single character.
		The regular expression [A-Z][a-z]* matches any word that starts with an uppercase letter and is followed by zero or more lowercase letters.
		The regular expression "[0-9]{3,}" specifies to match any integer number containing three or more digits: "123", "45678", etc. However, this regular expression does not match a one-digit or two-digit number.
	livedocs.macromedia.com /coldfusion/6/Developing_ColdFusion_MX_Applications_with_CFML/regexp3.htm (2452 words)

	Normal space : Normal regular space (Site not responding. Last check: 2007-11-07)
		X is a completely normal space if every subspace of X is normal.
		X is a perfectly normal space if every two disjoint closed sets can be precisely separated by a function.
		That is, given disjoint closed sets E and F, there is a continuous function f from X to the real line R such the preimages of {0} and {1} under f are E and F respectively.
	www.eurofreehost.com /no/Normal_regular_space_2.html (353 words)

	Algebraic geometry - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-07)
		In classical algebraic geometry, the main objects of interest are the vanishing sets of collections of polynomials, meaning the set of all points that simultaneously satisfy one or more polynomial equations.
		Just as continuous functions are the natural maps on topological spaces and smooth functions are the natural maps on differentiable manifolds, there is a natural class of functions on an algebraic set, called regular functions.
		It may seem unnaturally restrictive to require that a regular function always extend to the ambient space, but it is very similar to the situation in a normal topological space, where the Tietze extension theorem guarantees that a continuous function on a closed subset always extends to the ambient topological space.
	xahlee.org /_p/wiki/Algebraic_geometry.html (1675 words)

	Land Claim Recognition - Leveraging the Inherent Value of Lunar Land
		Land claims in space are addressed by the 1967 Outer Space Treaty and the 1979 Moon Treaty.
		Outer space, including the moon and other celestial bodies, is not subject to national appropriation by claim of sovereignty, by means of use or occupation, or by any other means.
		The exploration and use of outer space, including the moon and other celestial bodies, shall be carried out for the benefit and in the interest of all countries...and shall be the province of all mankind...and there shall be free access to all areas of celestial bodies.
	www.space-settlement-institute.org /Articles/LCRbrieftext.htm (2224 words)

	Wick Calculus for Regular Generalized Functions - Grothaus, Kondratiev, Us (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		It is shown that this calculus can be developed in a space of regular generalized functions.
		Its solution is shown to be a regular generalized process adapted to the standard version of Brownian motion.
		4 a dual pair of spaces of smooth and generalized random varia..
	citeseer.ist.psu.edu /grothaus98wick.html (595 words)

	[No title]
		Some time ago I had asked about polyhedra that tile space and got this response: ----------------------- Hop David observes that Euclidean 3-space can be monohedrally tiled with cubes, rhombic dodecahedra, truncated octahedra, triangular prisms, and hexagonal prisms and asks whether there are others.
		Leaving aside the tiling by rhombic dodecahedra, which is the dual of a uniform tiling by regular tetrahedra and octahedra, there are just five uniform monohedral tilings of Euclidean 3-space.
		These are the regular tiling {4, 3, 4}, with cubic cells; the "bitruncated" {4, 3, 4}, with truncated octahedral cells; the dual tilings {3, 6} x {oo} and {6, 3} x {oo}, with triangular or hexagonal prismatic cells; and one other tiling, by triangular prisms arranged in a different way.
	www.math.niu.edu /~rusin/known-math/01_incoming/fillspace (674 words)

	Regular Expression Sample Application - User Search
		Regular expressions specify patterns to search for in string data using standardized syntax conventions.
		Regular expressions provide a powerful method of identifying patterns of strings within a body of text.
		In addition this sample also shows how Regular Expressions can be used with Cursors These cursors are defined in the search.sql file, which uses different regular expression functions to extract the information from the USERINFO table.
	www.oracle.com /technology/sample_code/tech/pl_sql/regexp/usersearch/readme.html (548 words)

	Space A Changes Affect Europe
		Air Force News reports that regular space-available travel from Lajes to Italy and Spain will end Oct. 1, while a new stop finds its way onto the weekly channel route.
		However, there are multiple missions flying straight from Baltimore to Rhein Main AB both before and after missions through Lajes, Piott said.
		For a complete guide to Space A travel, see the Space A Travel guide.
	www.military.com /MilitaryReport/0,12914,MR_Space_090803,00.html (180 words)

	Housing: University Park (Site not responding. Last check: 2007-11-07)
		Transfer students and all upperclass students who did not enter the Online Contract System will be assigned permanent space in the order in which their contract was received and after students who did enter the process.
		Many students will be reassigned to regular space during fall semester, while some students may not be reassigned until the beginning of spring semester.
		If you are moving into a regular room, you are expected to move out of your supplemental space within four days of receiving your permanent assignment.
	www.hfs.psu.edu /residencehalls/supplemental.shtml (506 words)

	Tychonoff space (Site not responding. Last check: 2007-11-07)
		Tychonoff spaces are named after Andrey Tychonoff, whose Russian name (Тихонов) is also sometimes transliterated as "Tychonov", "Tikhonov", "Tihonov", or "Tichonov".
		is a completely regular space iff, given any closed set
		In particular, all subspacess and product spaces of Tychonoff or completely regular spaces have the same property.
	www.sciencedaily.com /encyclopedia/tychonoff_space (478 words)

	Problem A - Little Boxes (Site not responding. Last check: 2007-11-07)
		A regular box can be specified by giving the coordinates of the two points at the ends of one main diagonal (a diagonal that does not lie within any face).
		In this problem, you will be given some regular boxes and some points, about which you will compile some information.
		All numbers within a line will be separated by a single space, and there will be no spaces after the last number in a line.
	icpc.baylor.edu /Past/icpc99/Regionals/GNY98/prob_a.html (321 words)

	Beiträge zur Algebra und Geometrie/Contributions to Algebra and Geometry, Vol. 39, No. 2, pp. 497--516, 1998 (Site not responding. Last check: 2007-11-07)
		Abstract: Considering the regular dodecahedron tilings in the spaces of constant curvature we look for the fixed point free discrete transformation groups that act simply transitively on the tiles.
		Because of the large number of cases we modify the general algorithm and apply it for finding all the non-equivariant face identifications of a regular polyhedron, and for choosing those ones that generate fixed point free groups, if the number of polyhedra around the edges is given.
		So this paper gives a complete list of regular dodecahedral space forms, but in some small classes the difference of the manifolds (up to isometry) cannot be guaranteed yet.
	www.emis.de /journals/BAG/vol.39/no.2/24.html (299 words)

	Zero-gravity jet simulates space for regular folks - The Washington Times: Travel - October 30, 2004 (Site not responding. Last check: 2007-11-07)
		ABOARD G-FORCE ONE ABOVE THE GULF OF MEXICO — Space is the one frontier that's out of reach to the average person, but the feeling of space travel is now a little less elusive.
		For those who dream of rocketing into space or who just want a new thrill, roller-coaster-type flights aboard a modified jetliner give passengers the sense of walking on the moon and the ability to fly like Superman.
		It's these maneuvers, rather than the altitude — which is comparable to that of regular commercial flights — that cause the weightless effect.
	washingtontimes.com /functions/print.php?StoryID=20041029-075940-4763r (1123 words)

	A.P. Kombarov
		A space is called to have property D [4] if every countable closed discrete set has arbitrarily small closed neighborhoods.
		A regular space is said to have property wD [4] if every infinite closed discrete set has an infinite subset which has arbitrarily small closed neighborhoods.
		The exponential space \exp(X) is the set of all non-empty closed subsets of X with Vietoris (finite) topology.
	www.utm.edu /staff/jschomme/topology/c/a/a/h/55.htm (697 words)

	The Partnership - ch5-6
		By periodically putting small supplies of fuel aboard, it is possible to insure the station's long-term existence by switching on the engines and reestablishing the velocity lost as a result of braking in the upper layers of the atmosphere.
		The joined configuration of Soyuz and Salyut was 21.4 meters long with a total living space of 100 cubic meters, which gave the cosmonauts a place to conduct scientific experiments, relax, and sleep.
		Soviet space leaders were quick to reaffirm their plans to continue manned space flight.
	www.hq.nasa.gov /office/pao/History/SP-4209/ch5-6.htm (1620 words)

	The Times Herald - News - 01/12/2005 - Township to hold first regular Open Space Committee meeting (Site not responding. Last check: 2007-11-07)
		SKIPPACK - Skippack Township is scheduled to hold the first regular meeting of its Open Space Committee, a group charged with writing an open space plan that prioritizes land for acquisition and preservation by leveraging county funds.
		Though the money is intended for open space acquisition, the county also permits municipalities to build trails, or to spend up to 30 percent of their allotment for historic sites - known as heritage resources - and up to 50 percent on farmland acquisition, DeSipio said.
		The first task of the group will be writing an open space plan which includes sections evaluating previous open space efforts, assessing current resources and defining open space priorities.
	www.timesherald.com /site/news.cfm?newsid=13729057&BRD=1672&PAG=461&dept_id=33380&rfi=6 (524 words)

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