
	Where results make sense

Topic: Bounded lattice

Related Topics

upper bound

least upper bound

bounded rationality

bounded linear operator

bounded operator

free variables and bound variables

bounded complete

Prometheus Bound

lower bound

Brother Where You Bound

Bound movie

branch and bound

In the News (Fri 25 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Bounded lattice
		The set of compact elements of an arithmetic complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
		A bounded lattice for which every element has a complement is called a complemented lattice.
		These conditions basically amount to saying that there is a functor from the category of sets and functions to the category of lattices and lattice homomorphisms which is left adjoint to the forgetful functor from lattices to their underlying sets.
	www.algebra.com /algebra/about/history/Bounded-lattice.wikipedia (2389 words)

	Lattice (order)
		It will be stated explicitly whenever a lattice is required to have a least or greatest element.
		Since any lattice comes with two binary operations, it is natural to consider distributivity laws among them.
		One of the consequences of this statement is that the free lattice of a three element set of generators is already infinite.
	www.brainyencyclopedia.com /encyclopedia/l/la/lattice__order_.html (2552 words)

	Complemented lattice
		In the mathematical discipline of order theory, and in particular, in lattice theory, a complemented lattice is a bounded lattice (that is it has a least element 0 and a greatest element 1), in which each element x has a complement, defined as an element y such that
		Similarly, in an orthocomplemented lattice it can be shown that each element has exactly one complement - in fact, there is an idempotent order-reversing function from elements to their complements.
		Thus in a Boolean algebra, which is both a complemented distributive lattice and an orthocomplemented lattice, complements exist and are unique.
	www.algebra.com /algebra/about/history/Complemented-lattice.wikipedia (145 words)

	Lattice (order) - the free encyclopedia (Site not responding. Last check: 2007-11-01)
		Lattices constitute one of the most prominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions, such as semilattices, Heyting algebras, or
		arithmetic complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
		Consider a bounded lattice with greatest element 1 and least element 0.
	www.the-free-web-encyclopedia.com /default.asp?t=Lattice_%28order%29 (2113 words)

	php-deluxe.net - description Lattice order
		In mathematics, a lattice is a partially ordered set (or poset), in which all nonempty finite subsets have both a supremum (join) and an infimum (meet).
		Lattices can also be characterized as algebraic structures that satisfy certain identity.
		The set of compact elements of an arithmetic lattice complete lattice is a lattice with a least element, where the lattice operations are given by restricting the respective operations of the arithmetic lattice.
	www.php-deluxe.net /encyclopedia,index.page,Lattice-order.htm (1928 words)

	Lattice
		Every lattice can be generated from a basis for the underlying vector space by considering all linear combinations with integral coefficients.
		In another mathematical usage, a lattice is a partially ordered set in which all nonempty finite subsets have a least upper bound and a greatest lower bound (also called supremum and infimum, respectively).
		The lattice of submodules of a module and the lattice of normal subgroups of a group have the special property that x v (y ^ (x v z)) = (x v y) ^ (x v z) for all x, y and z in the lattice.
	www.fastload.org /la/Lattice.html (952 words)

	Bounded lattice (Site not responding. Last check: 2007-11-01)
		Lattices constitute one of the the mostprominent representatives of a series of "lattice-like" structures which admit order-theoretic as well as algebraic descriptions,such as semilattices, Heyting algebras, or Boolean algebras.
		For bounded lattices, preservation of least and greatest elements is just preservation of join and meet of the emptyset.
		Using the standard definition of isomorphisms as invertible morphisms, onefinds that an isomorphism of lattices is exactly a bijective latticehomomorphism.
	www.therfcc.org /bounded-lattice-215193.html (1889 words)

	Bounded (Site not responding. Last check: 2007-11-01)
		The term bounded appears in different parts of mathematics where a notion of "size" can be given.
		Therefore, a set is bounded if it is contained in a finite interval.
		A set S in a metric space (M, d) is bounded if it is contained in a ball of finite radius, i.e.
	www.nebulasearch.com /encyclopedia/article/Bounded.html (276 words)

	PlanetMath: complemented lattice
		A complemented lattice is a bounded lattice in which every element has a complement.
		In a complemented lattice, there may be more than one complement corresponding to each element.
		This is version 12 of complemented lattice, born on 2005-02-16, modified 2006-06-19.
	www.planetmath.org /encyclopedia/Complement2.html (178 words)

	Science Fair Projects - Scott domain
		Scott domains are very closely related to algebraic lattices, being different only in possibly lacking a greatest element.
		Since the empty set certainly has some upper bound, we can conclude the existence of a least element (the supremum of the empty set) from bounded completeness.
		It should be remarked that the property of being bounded complete is equivalent to the existence of all non-empty infima.
	www.all-science-fair-projects.com /science_fair_projects_encyclopedia/Scott_domain (701 words)

	Bounded, Diameter (Site not responding. Last check: 2007-11-01)
		The diameter of s is the least upper bound of x,y
		A set is totally bounded if it has a finite cover of ε-balls for every ε > 0.
		Let each of these lattice points be the center of an ε-ball, and the space is covered.
	www.mathreference.com /top-ms,bound.html (292 words)

	Citations: Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices - ... (Site not responding. Last check: 2007-11-01)
		It is known that lower bounded lattices form a proper subclass of the class of join semidistributive lattices.
		A lattice homomorphism h : K L is called a lower bounded homomorphism if for each a 2 L, fx 2 K : h(x) ag is either empty or....
		Likewise, an upper bounded lattice satisfies the dual property (SD) The lattice of convex subsets of a four element chain (Figure 1) provides an example of a lattice which satisfies (SD) but is not lower bounded.
	citeseer.ist.psu.edu /context/492992/0 (1389 words)

	Thomas Zaslavsky's Pub. List
		Main results: the number of regions, or bounded regions, of an affine real hyperplane arrangement, is determined by the (semi)lattice of flats through the characteristic polynomial, as is the number of regions of a projective real arrangement.
		"Bicircular geometry and the lattice of forests of a graph".
		Counting bounded lattice points not covered by an affinographic hyperplane arrangement is equivalent to bounded integral proper coloring of an integral gain graph.
	www.math.binghamton.edu /zaslav/Tpapers (2467 words)

	PlanetMath: bounded lattice
		A bounded lattice is one that is bounded both from above and below.
		Cross-references: lattice interval, meet, join, bounded, finite, lattice
		This is version 6 of bounded lattice, born on 2005-02-16, modified 2006-04-12.
	www.planetmath.org /encyclopedia/BoundedLattice.html (107 words)

	Kathleen Ollerenshaw Abstract
		In particular he has considered a circular quadrilateral bounded by arcs of equal circles which form a region resembling an asteroid.
		The region E is bounded by the arcs of four circles [±λ], [±μ], defined by the equations
		In the convenient terminology of figure-skating, the four defining circles form two "eights" with common centre and perpendicular axes: in fact, the particular domain arose out of demonstration of figure-skating on the frozen static-water tank of an Oxford college.
	www.scottlan.edu /lriddle/women/abstracts/ollerenshaw_abstract4.htm (200 words)

	Bounded continuous function on an open subset of R^n (Site not responding. Last check: 2007-11-01)
		Bounded continuous function on an open subset of R^n
		But I found this question and didn't understand why in the case of an open subset it shouldn't have been a complete space.
		Then the metric space of all bounded continuous maps from X to Y is complete.
	www.forum-one.org /new-6121885-4346.html (426 words)

	The Mizar abstract of LATTICE8
		O; end; definition let A be non empty set; let L be lower-bounded LATTICE; let d be BiFunction of A,L; let q be QuadrSeq of d; let O be Ordinal; func ConsecutiveDelta2(q,O) means :: LATTICE8:def 8 ex L0 being T-Sequence st it = last L0 and dom L0 = succ O and L0.
		l)`1; theorem :: LATTICE8:32 for A being non empty set for L be lower-bounded modular LATTICE for d be distance_function of A,L for S being ExtensionSeq2 of A,d for k,l being Nat st k <= l holds (S.
		l)`2; theorem :: LATTICE8:33 for L be lower-bounded modular LATTICE for S being ExtensionSeq2 of the carrier of L, BasicDF(L) for FS being non empty set st FS = union { (S.
	www.mizar.org /JFM/Vol12/lattice8.abs.html (432 words)

	The Basic Theory of Ordering Relations: A Supplement to Quantum Logic and Probability Theory
		A lattice L is said to be bounded iff it contains a smallest element 0 and a largest element 1.
		For instance, if L is the lattice of subspaces of 3-dimensional Euclidean space, then a complement for a given plane through the origin is provided by any line through the origin not lying in that plane.
		In particular, the subspace lattice of a vector space (of dimension greater than 1) is not distributive.
	plato.stanford.edu /entries/qt-quantlog/supplement2.html (1398 words)

	Topology - Wikipedia, the free encyclopedia
		, a set is compact if and only if it is closed and bounded.
		Occasionally, one needs to use the tools of topology but a "set of points" is not available.
		In pointless topology one considers instead the lattice of open sets as the basic notion of the theory, while Grothendieck topologies are certain structures defined on arbitrary categories which allow the definition of sheaves on those categories, and with that the definition of quite general cohomology theories.
	en.wikipedia.org /wiki/Topology (1876 words)

	PlanetMath:
		bounded exhaustion function (in exhaustion function) owned by jirka
		bounded linear map (in operator norm) owned by igor
		bounded operator (in operator norm) owned by igor
	planetmath.org /encyclopedia/B (1159 words)

	LMS Proceedings Abstract, paper PLMS 1530 (Site not responding. Last check: 2007-11-01)
		New criteria and Banach spaces are presented (for example, $GL$-spaces and Banach spaces with property $(\alpha)$) that ensure that the Boolean algebra generated by a pair of bounded, commuting Boolean algebras of projections is itself bounded.
		Also, for a Dedekind $\sigma $-complete Banach lattice $E$, the Boolean algebra consisting of all band projections in $E$ is $R$-bounded if and only if $E$ has finite cotype.
		In this situation, every bounded Boolean algebra of projections in $E$ is $R$-bounded and has a Bade complete strong closure.
	www.lms.ac.uk /publications/proceedings/abstracts/p1530a.html (145 words)

	lattice_(order) - The Wordbook Encyclopedia (Site not responding. Last check: 2007-11-01)
		That article also discusses how one may rephrase the above definition in terms of the existence of suitable Galois connections between related posets — an approach of special interest for the category theoretic approach to lattices.
		Using the standard definition of universal algebra, a free lattice over a generating set S is a lattice L together with a function i:S?
		L, such that any function f from S to the underlying set of some lattice M can be factored uniquely through a lattice homomorphism f° from L to M.
	www.thewordbook.com /lattice_(order) (2372 words)

	JKU-FoDok Forschungsdokumentation der Universität Linz - Publikation - A note on ordinal sums of t-norms on bounded ...
		Susanne Saminger, Erich Peter Klement, Radko Mesiar, "A note on ordinal sums of t-norms on bounded lattices", Proceedings of Joint 4th Int.
		Ordinal sums of t-norms on bounded lattices are discussed.
		Moreover, we obtain a t-norm also if the underlying lattice is an ordinal sum (in the sense of Birkhoff) of the carriers of the summands.
	fodok.jku.at /fodok/publikation.xsql?PUB_ID=20876 (220 words)

	More on the meanderings of mangabeys; how to test whether bounded walks are random. (Site not responding. Last check: 2007-11-01)
		More on the meanderings of mangabeys; how to test whether bounded walks are random.
		Restricting movement to a square lattice is a reasonable approximation even when rectangular boundaries are incorporated.
		In conclusion, there are better approaches to establish whether boundaries exist and whether movements follow a random walk.
	www.stats.bris.ac.uk /research/stats/pub/ResRept/1999/mangabeys.html (203 words)

	Boolean Algebra
		Bounded distributive lattice (S, +, ·, 0, 1), x'' = x, 0' = 1, x' · x = 0 and x' + x = 1.
		Bounded lattice with (c · x) < a iff x < (c
		Each bounded distributive lattice is represented as the lattice of compact open sets of its spectrum, a coherent space.
	orion.math.iastate.edu /jdhsmith/class/M567Defn.htm (758 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		The collection of possible sets of parameters for orthogonal arrays with N runs has a natural lattice structure, induced by the ``expansive replacement'' construction method.
		To get a sense for the number of dual atoms, and to begin to understand the lattice as a function of N, we investigate the height and the size of the lattice.
		On the other hand, the number of nodes in the lattice is bounded above by a superpolynomial function of N (and superpolynomial growth does occur for certain sequences of values of N).
	www.research.att.com /~njas/doc/rao.txt (248 words)

	mp_arc 95-415 (Site not responding. Last check: 2007-11-01)
		We also discuss the band spectra for rectangular lattices with the mentioned couplings.
		We show that they roughly correspond to their Kronig-Penney analogues: the delta' lattices have bands whose widths are asymptotically bounded and do not approach zero, while the delta lattice gap widths are bounded.
		However, if the lattice-spacing ratio is an irrational number badly approximable by rationals, and the delta coupling constant is small enough, the delta lattice has no ggaps above the threshold of the spectrum.
	www.ma.utexas.edu /mp_arc-bin/mpa?yn=95-415 (195 words)

	[No title] (Site not responding. Last check: 2007-11-01)
		: For all elements x and y of L, the set has both a least upper bound in L (join, or supremum) and a greatest lower bound in L (meet, or infimum).
		The join and meet of x and y are denoted by x \vee y and x \wedge y, respectively.
		Here you can find a list of the authors.
	www.maxpedia.org /cgi-bin/mp/m.pl?la=en&sw=Lattice+(order) (275 words)

	Publications of the SPACES team
		It also gives improved bounds in some cases, and examples showing that those new bounds are optimal.
		If d is a bound on the degrees and t a bound on the bitsize of the minors extracted from Sylvester matrix, our algorithm has O(d2) arithmetic operations and size of intermediate computations 2 t.
		The key idea is to precise the relations between the successive Sylvester matrix of A and B in one hand and of A and XB on the other hand, using the notion of G-remainder we introduce.
	www-calfor.lip6.fr /~safey/Spaces/publications.html (13078 words)

Try your search on: Qwika (all wikis)