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Topic: Completely regular

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	Tychonoff space - Wikipedia, the free encyclopedia
		X is a completely regular space if and only if, 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.
		Completely regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence.
		Complete regularity and Tychonoff-ness are preserved by taking initial topologies.
	en.wikipedia.org /wiki/Completely_regular_space (629 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.
		Most topological spaces studied in mathematical analysis are regular; in fact, they are usually completely regular, which is a stronger condition.
		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 (948 words)

	Tychonoff space
		In topology and related brances of mathematics, Tychonoff spaces and completely regular spaces are particularly nice kinds of topological spaces.
		On the other hand, a space is completely regular iff its Kolmogorov quotient is Tychonoff.
		Every locally compact regular space is completely regular, and every locally compact Hausdorff space is Tychonoff.
	www.ebroadcast.com.au /lookup/encyclopedia/ty/Tychonov_space.html (401 words)

	PlanetMath: separation axioms
		See Also: normal, Hausdorff space not completely Hausdorff, Sierpinski space, metric spaces are Hausdorff, zero dimensional, Hausdorff space, regular space,
		Cross-references: counterexamples, strictly, implications, completely regular space, Hausdorff space, Fréchet space, satisfies, Urysohn function, closed set, closures, disjoint, contain, neighborhood, points, pathological, open sets, separated, topological space
		In this convention normal, regular is defined as the
	planetmath.org /encyclopedia/Regular.html (508 words)

	[No title]
		On congruence lattices of regular semigroups, J. Algebra 82, (1983), pp.
		On the lattice of varieties of completely regular semigroups, J. Australian Math.
		The Howson property in varieties of completely regular semigroups, Simon Stevin, 63 (1989), 285-294 (with P. Trotter).
	www.mscs.mu.edu /~jones/papers_deroff (792 words)

	NetCDF Coordinate Conventions: netCDF and "complex" data
		REGULAR GRIDS To import scalar data on a regular grid, specify the netCDF file name as the "name" parameter in the Import module.
		A regular grid is assumed, with the origin at 0.0, and a spacing of 1.0 along each axis.
		Regular positions can be specified with just the origin and spacing between grid points along each axis in compact form.
	www.unidata.ucar.edu /staff/russ/netcdf/coords/0023.html (3271 words)

	Picking Up Perl - Regular Expressions
		To remedy that, this chapter is devoted completely to regular expressions.
		Regular expressions are a concept borrowed from automata theory.
		If a regular expression "matches" a given string, then that string is in the class we described with the regular expression.
	www.faqs.org /docs/pperl/pickingUpPerl_7.html (1061 words)

	Peter Trotter's Home Page
		Varieties of completely regular semigroups and of inverse semigroups, e-varieties and pseudovarieties.
		Congruences on regular and completely regular semigroups, J. Austral.
		Weil) The lattice of pseudovarieties of idempotent semigroups and a non-regular analogue, Algebra Universalis 37 (1997), 491-526
	www.maths.utas.edu.au /People/Trotter/HomePage.html (855 words)

	AMCA: Planar Completely Regular Continua with Structure by S. S. Zafiridou (Site not responding. Last check: 2007-10-01)
		A metric continuum K is called completely regular if each nondegenerate subcontinuum of K has nonvoid interior.
		A completely regular continuum with structure ([K\tilde], [F\tilde], [A\tilde]) is said to be universal for a family
		We shall prove that in the class of all planar completely regular continua with structure there is no universal element.
	at.yorku.ca /c/a/b/c/30.htm (266 words)

	[No title] (Site not responding. Last check: 2007-10-01)
		Beside the trajectories that generates the two main regular islands and the chaotic sea there are an infinite number of other stable and unstable trajectories present and some examples are shown in Figs.
		The nature of the phase space (regular, chaotic, or mixed) is shown to influence the statistics of the spectra of the wave systems.
		Spectra of completely regular systems (square or circle billiard) obey the "Poisson" statistics, while spectra of completely chaotic ones (stadium billiard) obey a different statistics the "GOE" (Gaussian Orthogonal Ensemble) statistics.
	physics.clarku.edu /~akudrolli/clover.html (477 words)

	Volume 24, Number 1, 1998
		We present the original proof, based on the Doitchinov completion, that a totally bounded quiet quasi-uniformity is a uniformity.
		A characterization (in the spirit of M. Lodato [23, 24]) of the proximity relations induced by the regular extensions is given.
		A new class of regular spaces, called CE-regular spaces, is introduced; the class of all OCE-regular spaces of J. Porter and C. Votaw [29] (and, hence, the class of all regular-closed spaces) is its proper subclass.
	www.math.bas.bg /~serdica/n1_98.html (1107 words)

	[No title] (Site not responding. Last check: 2007-10-01)
		Extensions are done, not by doing a completely new design, but in terms of the original system -- it may not be perfect, but it's good enough to allow people to move on and do other things.
		If we have a large, complex regular expression that is used multiple times in some other, containing regular expression, we can name it, using the binding forms of the embedding language (e.g., Scheme), and refer to it by name in the containing expression.
		After all, regular sets are closed under these operations, and they are useful, so they should be in the toolkit.
	www.cc.gatech.edu /~shivers/papers/sre.txt (9318 words)

	Level Repulsion (Site not responding. Last check: 2007-10-01)
		Note that the spacing here is not as random as the left, but also not as regular as the right.
		When the spacings of the middle plot are analyzed in the same manner, the resulting graph follows a function called the Wigner spacing distribution.
		The spacing distribution of the middle plot is thus a combination of two ideal cases: completely random and completely regular.
	www.nscl.msu.edu /~brown/beauty/Spacing/spacing.html (516 words)

	Insurance Basics, Ch. 3: Make sure you're completely protected
		Regular policies often exclude certain disasters like earthquakes or floods, or put a ceiling on the dollar amounts they'll pay for certain items like jewelry or antiques.
		Whichever method you use, be sure to update your inventory periodically to allow for those new purchases like that plasma TV or new computer.
		And keep a copy in a safe place away from the house, so that if you have a complete loss (fire, flood, tornado), you'll be able to get your hands on it.
	www.bankrate.com /goocan/green/insurance/basics3-2a.asp?caret=8 (626 words)

	Dr. Dobb's \| Regular Expressions \| April 11, 2006
		Sure, regular expressions are useful to search through source files to find the places where some member function is called, or to replace one thing with another, so it's handy to have a regular expression interpreter built in to your text editor.
		The one thing to keep in mind when writing a regular expression is that both C++ and the regular expression machinery give special meaning to a backslash character.
		It then changes the regular expression object to hold an expression that matches a sequence of characters that are not separators, followed by one or more separators or by the end of the target text.
	www.ddj.com /dept/cpp/185300414 (3158 words)

	Springer Online Reference Works
		-space is always regular and is called normal (cf.
		A space in which every point is functionally separable from every closed set not containing it is called completely regular (cf.
		The adjective "completely regular" is often associated with the letter
	eom.springer.de /s/s084520.htm (262 words)

	Topology/Separation Axioms - Wikibooks, collection of open-content textbooks
		A topological space that is both completely regular and T
		Complete regularity always implies regularity, even without assuming T
		A topological space is completely normal if and only if every subspace is normal.
	en.wikibooks.org /wiki/Separation_Axioms (641 words)

	[No title] (Site not responding. Last check: 2007-10-01)
		T_2.5 spaces are sometimes called completely Hausdorff spaces or Urysohn spaces.
		Subject: Re: regular 2nd countable spaces Date: Fri, 3 Aug 2001 16:10:11 -0500 Newsgroups: sci.math I am accustomed to T_2.5 meaning completely Hausdorff or Urysohn in the stronger sense, viz., for any two points p != q there is a continuous function into [0,1] with f(p) = 0 and f(q) = 1.
		Yes, I think I got 'completely Hausdorff' and 'Urysohn' mixed up - 'Urysohn' is usually used in the weaker sense and 'completely Hausdorff' in the stronger sense (although I've seen them the other way around too).
	www.math.niu.edu /~rusin/known-math/01_incoming/T_n (430 words)

	[No title]
		346 insert an improved definition of complete regularity in arbitrary graphs.
		.SC Brouwer.[[ Brouwer 1990 completely regular codes note.]]) showed that for distance-regular graphs this definition is equivalent to the one given in \(sc11.1, and it is often much easier to work with.
		.Eop.R The Goethals-Seidel graph is strongly regular of rank 6, so $roman E$ is not distance-transitive; in fact the subconstituent of size 216 splits into two suborbits, of sizes 24 and 192, respectively.
	www.win.tue.nl /~aeb/drg/ch11 (1360 words)

	Regular space
		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.
		Suppose that A is a set in a topological space X and f is a continuous function from A to a regular space Y.
		Suppose that, whenever a net or filter in A converges to a point in X (say x = lim
	www.ebroadcast.com.au /lookup/encyclopedia/t3/T3_space.html (917 words)

	Spanish Grammar: regular verbs part two
		Remember, all Spanish verbs are either "regular" or "irregular." In this lesson we continue by looking at our three model verbs, which are completely regular:
		Remember that when you conjugate a verb, you mold the infinitive to match the subject of the sentence.
		In this lesson, you will learn to conjugate regular verbs for the following forms: you (familiar), he, she, you-all (familiar) and they.
	www.studyspanish.com /lessons/regverb2.htm (643 words)

	Carnegie Mellon Near-Regular Texture Database (Site not responding. Last check: 2007-10-01)
		It covers the spectrum of textures from completely regular to near-regular to irregular.
		These are textures which are regular enough such that they could be in the "Regular Textures Sorted by the 17 Wallpaper Groups" database but they were added more recently.
		The textures in this gallery tend to have little geometric distortions, thus their lattice could be detected with relative ease compared to geometrically distorted NRTs.
	graphics.cs.cmu.edu /data/texturedb/gallery (409 words)

	Completely Regular Spaces
		I have seen two different definitions of "completely regular" (one in my class and online, and the other in my textbook).
		A space S is said to be completely regular if for every closed subset C of S and every point x in S-C there is a continuous function from S to I such that
		A space S is said to be completely regular if for every point p of S and for every open set U containing p, there is a continuous function of S into I such that f(p)=0 and f(x)=1 for all points x in S-U. Cincinnatus
	www.physicsforums.com /showthread.php?t=97247 (209 words)

	Janusz Konieczny's Publications
		Regular, Inverse, and Completely Regular Centralizers of Permutations, Mathematica Bohemica 128 (2003), 179-186.
		Molaei's Generalized Groups Are Completely Simple Semigroups (with J. Araujo), Bulletin of the Polytechnic Institute of Jassy 48(52) (2002), 1-5.
		Green's Relations and Regularity in Centralizers of Permutations, Glasgow Mathematical Journal 41 (1999), 45-57.
	people.umw.edu /~jkoniecz/jkpubl.htm (323 words)

	FAH Excerpt: Separation (Site not responding. Last check: 2007-10-01)
		Normality is an interesting condition by itself --- we shall introduce it in 16.26 --- but it fits in the chart only in conjunction with the symmetry condition, since normal by itself does not imply completely regular.
		space'', and ``completely regular Hausdorff space'' are used interchangeably in the literature; they all describe the same thing.
		Most of the separation and regularity axioms are well known, and can be found in many topology books.
	www.math.vanderbilt.edu /~schectex/ccc/excerpts/separat.html (481 words)

	What is a normal cycle: iVillage
		Actually, completely regular, predictable cycles are more unusual than ones that vary.
		In some ways, you could say that you may be more fertile, because the fact that you have such regular cycles means that you are probably ovulating every single cycle, which you cannot necessarily say of women with irregular cycles.
		If your friends were taught how to chart their cycles through observing their three main fertility signs (waking temperature, cervical fluid and cervical position) they would be able to ultimately know if and when they were fertile in any given cycle, or certainly determine if there may be a problem conceiving, which they can resolve.
	www.ivillage.co.uk /pregnancyandbaby/fertility/conception/qas/0,,4_162311,00.html?dst=rss\|ukpre (271 words)

	Extra problems (Site not responding. Last check: 2007-10-01)
		They are RECOMMENDED to those who does well the regular homework.
		Please handle your solutions separately from your regular homework, marking them with the problem name.
		Then a solution may be posted, and no credit will be given for the problem after that.
	www.math.purdue.edu /~eremenko/extra.html (124 words)

	DAY 3: Goofy Versus Regular - Regular Foot Wins!
		When the individual session was over, the regulars led by 41 points, not bad considering the score was 1161 to 1119.
		Leo Romero and Kurtis Colamonica were a big part of the Regular footed victory but Bastien was the clear MVP for the regular footers.
		Backside flips, big flips, cab kick flips, double kick flips, and a big flip to front board to fakie down the rail were just a few of the tricks that had everyone amazed at Bastien’s runs.
	www.skateboardermag.com /skateboarder-news-features/news/gvr3/index.html (517 words)

	Roger Guimera Research
		For a long time, such networks where modeled either as completely regular or as completely random.
		Although in some cases these approximations are essentially correct, in many cases they do not work at all.
		Definitely, they are not completely random or completely ordered.
	amaral.northwestern.edu /roger/research_networks.html (283 words)

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