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Topic: Stone spaces

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	Stone duality - Wikipedia, the free encyclopedia
		Probably the most general duality which is classically referred to as "Stone duality" is the duality between the category Sob of sober spaces with continuous functions and the category SFrm of spatial frames with appropriate frame homomorphisms.
		Stone's representation for distributive lattices can be extended via an equivalence of coherent spaces and Priestley spaces (ordered topological spaces, that are compact and totally order-disconnected).
		It is common to abbreviate this space as pt(L).
	en.wikipedia.org /wiki/Stone's_duality (2047 words)

	Stone Valley Recreation Area \| Rules & Regulations (Site not responding. Last check: 2007-11-06)
		The Stone Valley Recreation Area Staff are authorized to inspect for compliance to fishing and boating regulations of the Pennsylvania Fish and Boat Commission.
		Rental boats are limited to use on Stone Valley Lake and cannot be removed from the immediate area.
		Sailboat crews are to be properly positioned in the boat and are not to sit on the sailboat's bow deck (foredeck).
	www.psu.edu /Stone_Valley/rules.htm (346 words)

	Backgammon Rules, How to Play - Poker.com (Site not responding. Last check: 2007-11-06)
		A stone is entered by moving it to an open point corresponding to one of the numbers on the rolled dice.
		A player bears off a stone, by rolling a number that corresponds to the point on which the stone resides, and then removing that stone from the board.
		More so, if the loser has not borne off any of his stones and still has a stone on the bar or in the winners` home board, he is backgammoned and loses three times the value of the doubling cube.
	www.poker.com /rules_backgammon.htm (1396 words)

	Project for Public Spaces (PPS) \| Stone Soup: Mobilizing Hidden Assets for Park Revitalization
		They built a pile of kindling and logs at the center of the town square, and asked the town flsmith if they could borrow a very large pot, which they placed atop the wood, then filled the pot half full with water from the village well.
		Three stones from a nearby field were then very ceremoniously added to the pot, and the fire beneath was lit.
		Stone Soup Park has been overrun by prostitutes and drug dealers for years, and lately it's become even more of a wasteland of violence and despair.
	pps.org /topics/community/thecommunity/stone_soup (1686 words)

	[No title]
		If a silver mine action card is turned over, each player moves his power stone one space forward on the power track for each mountain range that he has enclosed in his territories.
		The other spaces are not viable due to being separated by a boundary or due to their containing a mountain.
		The spaces in the territory are counted and will be cross referenced on the territory founding table with the power points.
	www.fortunecity.com /boozers/brewerytap/1/lh2.txt (3234 words)

	Stone's representation theorem for Boolean algebras - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, Stone's representation theorem for Boolean algebras, named in honor of Marshall H. Stone, is the duality between the category of Boolean algebras and the category of Stone spaces, i.e., totally disconnected compact Hausdorff topological spaces (also known as Boolean spaces).
		Stone's duality generalises to infinite sets of propositions the use of truth tables to characterise elements of finite Boolean algebras.
		In detail, the Stone space of a Boolean algebra A is the set of all 2-valued homomorphisms on A, with the topology of pointwise convergence of nets of such homomorphisms.
	en.wikipedia.org /wiki/Stone's_representation_theorem_for_Boolean_algebras (534 words)

	[No title]
		You surround a stone by filling in the spaces around it - a stone can be surrounded by any combination of your stones, your opponent's stones and the edge of the board.
		Remember that your stones can be surrounded by your own stones, as well as your opponent's stones and the edge of the board.
		Remember, if one of your stones is surrounded on your own turn (even if you surround one of your opponent's stones at the same time), you lose the game.
	www.stephen.com /sue/sue_man.txt (3023 words)

	Using Stone Weierstrass
		Let s be the completion of m with respect to the second norm, hence s is a hilbert space.
		This satisfies the conditions of stone weierstrass, and the closure of w, under the uniform norm, is all of m.
		Let m be the ring of continuous functions from d into R, and let s be the completion of this ring, which includes piecewise continuous periodic functions, such as the square wave.
	www.mathreference.com /top-ban,stone.html (1342 words)

	Gamedek.com - Game Rules: Chess, Backgammon, Mah Jongg, Solitaire and more.
		A stone can only be moved to an open point (one not occupied by two or more opposing stones).
		If there are no stones on higher-numbered points, the player is can remove a stone from the highest point one of his stones sits on.
		Or, worse, if the loser has not borne off any of his stones and still has a stone on the bar or in the winner's home board, he is backgammoned and loses three times the value of the doubling cube.
	www.gamedek.com /Rules/rules.html (3953 words)

	Stone Age Building
		The spaces between the houses was filled with rubbish and turf for some kind of protection against the wind.
		Between the dresser and the central hearth, is a stone seat.
		During excavation a lot of stones fractured by heat and fragments of chert were found.
	www.missgien.net /stone-age/skarabrae.html (842 words)

	Stone Valley Recreation Area \| Text Only Version (Site not responding. Last check: 2007-11-06)
		The wood and stone buildings are in harmony with the natural beauty of the valley, rich with hardwood, conifers, and wildlife.
		With the completion of the dam in 1960, and the allocation of 574 acres of land in the Stone Valley Tract for recreational development, the Stone Valley Recreation Area was initiated.
		Stone Valley's Picnic Pavilion is available for rental April through October for university and non-university groups.
	www.psu.edu /dept/Stone_Valley/textonly.htm (3272 words)

	Abstract Stone Duality (Site not responding. Last check: 2007-11-06)
		Abstract Stone Duality (ASD) is a type theory in which the topology on a space is an exponential with a lambda-calculus, not an infinitary lattice.
		Stone also told us always to look for the topology on a mathematical construction, even one whose data come from discrete algebra [23].
		By Stone duality, the opposite of the category C of ``spaces'' is to be a category of ``algebras'', but defined by a monad over C rather than over sets.
	www.cs.man.ac.uk /~pt/ASD/manifesto.html (2776 words)

	Backgammon - MSN Games - Free Online Games
		To win, be the first player to move all your stones around the board to your home table, and then bear them off the board before your opponent bears off his or her own.
		Each player has 15 stones of one color that are placed along the 24 points (the triangular spaces) on the board.
		The player with the higher number goes first, moving the stone(s) according to the number of spots, or pips, showing on both dice.
	zone.msn.com /en/backgammon/article/bckglearntoplay1 (369 words)

	Domains and Lambda Calculi (book announcement)
		In this book we aim to present in an elementary and unified way the theory of certain topological spaces, best presented as order theoretical structures, that have proved to be useful in the modelling of various families of typed lambda-calculi considered as core programming languages and as meta-languages for denotational semantics.
		We develop the theory along the lines of chapters 1 and 3: we study stability on meet cpo's, dI-domains and event structures (and coherence spaces), stable bifinite domains (with an application to the construction of a retraction of all retractions), and continuous L-domains.
		The simplest framework for stability, coherence spaces, led Girard to the discovery of a new resource-sensitive logic.
	www.cis.upenn.edu /~bcpierce/types/archives/1997-98/msg00317.html (1798 words)

	Partializing Stone Spaces using SFP domains (Site not responding. Last check: 2007-11-06)
		In this paper we investigate the problem of ``partializing'' Stone spaces by SFP domains.
		More specifically, we introduce a suitable subcategory SFPm of SFP, which is naturally related to the special category of Stone spaces 2-Stone, by the functor MAX, which associates to each object of SFPm the space of its maximal elements.
		Using the notion of ``rigid'' embedding projection pair, we show that the two domains are not isomorphic, thus providing a negative answer to an open problem raised in their paper by Mislove, Moss and Oles.
	www.di.unipi.it /~baldan/Papers/Abstract/Stone.html (174 words)

	PH. D. THESIS
		In the thirties, Stone presented in the famous papers [The theory of representation for Boolean algebras, Trans.
		In parallel, with the aim of completing for frames a picture analogous to the one for spaces, we characterize uniform structures in terms of "gauge structures", that is, families of metric diameters satisfying certain axioms.
		Nauk 76 (1951) 341-343] are also studied in the context of frames and the chapter ends with a remark which once more exhibits the adequacy of Weil entourages to bring out the meaning, in the context of frames, of the spatial results formulated in terms of entourages.
	www.mat.uc.pt /~picado/publicat/Intr.html (2247 words)

	AMCA: Finite Approximation of Compact Hausdorff Spaces by R.G. Wilson
		However, our goal here is not simply to study finite spaces, but to use them to approximate other (infinite) topological spaces.
		We will also show that approximators of compact Hausdorff spaces also arise in a familiar way as Stone spaces of Boolean algebras.
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/a/o/86.htm (546 words)

	Stonelight Introduction
		In early 1995, thanks to Washington, D.C. photographer and teacher Charles Rumph, I became fascinated with the interaction of light and stone, particularly in voluminous spaces created by fashioned structures such as castles, cathedrals, forts, mills, and the like.
		Of greatest interest are spaces where there appears to me to be a special harmony in the way in which stone is worked both aesthetically and functionally.
		Somewhere in and around such places and at least for some part of the day, the light appears not just to reflect from the stone but also to emanate from it, creating sometimes complex but always mystifying combinations of light and shadow.
	www.stone-light.com /page25.htm (216 words)

	Stone Conference \| Prismatique Designs Ltd. (Site not responding. Last check: 2007-11-06)
		Stone Conference - For boardroom and high image conference rooms the Konverse product series with stone tops offers an affordable, elegant alternative to traditional wood veneer table choices.
		Our experience in stone conference table construction makes for a simplified, "turn-key" process where we manufacture and supply all components and incorporate unique handling and packaging techniques to ensure a quality application.
		Our flexibility in stone tables is hard to beat - unlimited sizes and shapes, three base options, five edge choices in two thicknesses, multiple technology interface units for electrical/communication needs and engineering support to evaluate customized requirements.
	www.prismatique.com /stone_features.htm (157 words)

	CiteULike: Tag stone (Site not responding. Last check: 2007-11-06)
		Geographic variation and environmental risk factors for the incidence of initial kidney stones in patients with spinal cord injury.
		Bladder management and risk of bladder stone formation in spinal cord injured patients.
		Stone spectra of finite von Neumann algebras of type $I_n$
	www.citeulike.org /tag/stone (141 words)

	Susan (Site not responding. Last check: 2007-11-06)
		The -large option starts a game on a hexagonal board with 6 spaces on each side of the hexagon, for a total of 91 spaces.
		The default board (shown in the rules) has 5 space on each side with 61 total spaces.
		The computer is developing a pattern to make my stone at e5 a liability.
	www.gamerz.net /~pbmserv/susan.html (3122 words)

	2003 Tbilisi Logic Conference Abstracts
		for every Stone space X, the set K(X) endowed with the Vietoris topology is a Stone space, and for every continuous map f between Stone spaces, the map that assigns any F in K(X) to its direct image f[F] gives a continuous map between the associated Vietoris spaces.
		The Sierpinski space is defined as that object classifying both open and closed subspaces, and the double power space functor is axiomatized to be double exponentiation with respect to Sierpinski.
		We determine natural and expressive fragments of MS which are decidable in various classes of distance spaces validating the triangular inequality, in particular, the class of all metric spaces.
	sierra.nmsu.edu /morandi/TbilisiConference/Abstracts.html (2014 words)

	Backgammon For Money - www.Backgammon-for-money.com
		In both ways there is a stake involved in the game and the winner takes everything and pays a small fee.
		Hitting and Entering A point occupied by a single stone of either color is called a blot.
		Bearing Off Once a player has moved all of his fifteen stones into his home board, he can begin bearing off.
	www.backgammon-for-money.com (1155 words)

	Stone Table Top Fountains - Built with strong, heavy materials, these stone tabletop fountains are built to last
		Stone Table Top Fountains - Built with strong, heavy materials, these stone tabletop fountains are built to last
		The integrity of stone brings a timeless, classic quality to any space, and these stone fountains are made in compact tabletop sizes so that you can enjoy their beauty in smaller spaces.
		Our stone tabletop fountains bring the natural, understated elegance of granite and other stones into your home or office in soothing, creative, contemplative designs.
	www.kineticfountains.com /stone-tabletop-fountains.asp (152 words)

	[No title]
		There are many granite stones which will probably look the same in 100 years as they did 100 years ago.
		Several of the graves had recognition markers, i.e veterans, G.A.R., etc., which were all metal markers stuck in the ground near the headstone.
		Remarkably these were intact, as were metal funeral home markers used pending placement of a stone.
	skyways.lib.ks.us /genweb/archives/lyon/cem/catholic.txt (880 words)

	Country wedding, rehearsal dinner, and reception center in Little Compton, Rhode Island (Site not responding. Last check: 2007-11-06)
		The Stone House Club is situated grandly on Sakonnet Point in beautiful Little Compton, Rhode Island.
		A favorite swan haunt, our country setting attracts a wide variety of bird life, enamored of our generous spaces.
		We have refashioned a magnificent old barn into wonderful party, meeting, and living spaces.
	www.stonehouseclub.com /weddings.htm (372 words)

	AMCA: Duality as a Unifying Framework by Ingrid Rewitzky, Hilary Priestley, Mai Gehrke, Achim Jung, Marcello Bonsangue
		Duality theory as unifying framework for modal logics Marcello Bonsangue (LIACS, Leiden University) The aim of this talk is to describe a framework for the use of dualities for a coalgebraic semantics of modal logic.
		We apply the framework to Vietoris coalgebras on topological spaces, using the duality between spaces and observation frames, to obtain sound and complete modal logics for Posets, Sets, spectral spaces, Stone spaces and various categories of domains.
		A hierarchy of Stone dualities Achim Jung (Department of Computer Science, University of Birmingham) Stone's classical representation theorem (1936/37) associates with every Boolean algebra a compact totally disconnected space (now commonly referred to as a "Stone space").
	at.yorku.ca /c/a/o/p/07.htm (954 words)

	Etched in Stone - Our Product (Site not responding. Last check: 2007-11-06)
		This type of stone is often the choice for outdoor applications like golf courses, pro-perty development, corporate identification, etc. These stones are often available locally where their use is required.
		And while it is probably not as aged as Stonehenge, it still has a record of endurance with a building date of 1254 B.C. The summary: Sandstone has withstood the test of time and weather as a building material.
		Coloration: Our process of coloration was developed specifically for stone applications and is designed to be absorbed into the stone's pore spaces.
	www.etchedinstone.info /product2.htm (290 words)

	Table of contents for Library of Congress control number 2002280831
		REPRESENTATION OF BOOLEAN ALGEBRAS 125 1 The Stone Theorem 125 2 Interpretation of the basic notions of the theory of Boolean algebras in the language of Stone spaces 136 3 Stone functors 150 4.
		The space 6y as the family of resolutions of the identity.
		EXISTENCE OF A MEASURE 391 1 Conditions for existence of a measure 391 2 Existence of a measure invariant under the automorphism group 399 3 The Potepun Theorem 417 4 Automorphisms of normable algebras and invariant measures 433 5 Construction of a normed Boolean algebra given a transformation group 439 9.
	www.loc.gov /catdir/toc/fy031/2002280831.html (444 words)

	DISSERTAÇÃO DE DOUTORAMENTO
		Foi Isbell no famoso artigo de 1972 "Atomless parts of spaces" que primeiro salientou isto e primeiro apontou para a necessidade de uma terminologia separada para a categoria dual da dos reticulados locais, cujos objectos, como atrás citado, designou por "locales".
		Johnstone em [Stone spaces, Cambridge University Press, 1982], [The point of pointless topology, Bull.
		A good example is the concept of topological spaces: compare such "competing" concepts as metric spaces, convergence spaces, pseudotopological spaces, uniform spaces, nearness spaces, frames respectively locales, etc. What are the structural "necessities" or at least "desirabilities"?
	www.mat.uc.pt /~picado/publicat/Pref.html (2782 words)

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