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Bounded complete - Wikipedia, the free encyclopedia Bounded completeness then yields the existence of a least upper bound of any "consistent" subset, which can be regarded as the most general piece of information that captures all the knowledge present within this subset. Bounded completeness has various relationships to other completeness properties, which are detailed in the article on completeness in order theory. Hence it is important to distinguish between a bounded complete poset and a bounded cpo. en.wikipedia.org /wiki/Bounded_complete   (441 words)

Completeness (order theory)   (Site not responding. Last check: 2007-11-07) All completeness properties are described along a similar scheme: one describes a certain class of subsets of a partial order that are required to have a supremum or infimum. Although concepts with the names "complete" and "bounded" were already defined, confusion is unlikely to occur since one would rarely speak of a "bounded complete poset" when meaning a "bounded cpo" (which is just a "cpo with greatest element"). Consequently, bounded completeness is equivalent to the existence of all non-empty lower bounded infima. www.serebella.com /encyclopedia/article-Completeness_(order_theory).html   (2056 words)

Complete partial order - Wikipedia, the free encyclopedia A complete partial order (cpo) is a dcpo with a least element. For instance, theorems involving directed completeness (and characterizations thereof) are to be found in the articles on continuous posets, algebraic posets, and the Scott topology. All complete lattices are of course also directed complete and thus provide numerous (though not particularly instructive) examples for dcpos. www.wikipedia.org /wiki/Complete_partial_order   (515 words)

Completeness - Wikipedia, the free encyclopedia It should be noted that "complete" here is just a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion". Furthermore, an ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field, which should be compared to the (slightly different) order-theoretical notion of bounded completeness. In computational complexity theory, a problem P is complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction. en.wikipedia.org /wiki/Complete   (675 words)

Bounded complete -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07) Bounded completeness has various relationships to other completeness properties, which are detailed in the article on (Click link for more info and facts about completeness in order theory) completeness in order theory. Note also that the term bounded poset is sometimes used to refer to a partially ordered set which has both a (Click link for more info and facts about least) least and a (Click link for more info and facts about greatest element) greatest element. Hence it is important to distinguish between a bounded complete poset and a bounded (Click link for more info and facts about cpo) cpo. www.absoluteastronomy.com /encyclopedia/B/Bo/Bounded_complete.htm   (461 words)

Scott domain - Wikipedia, the free encyclopedia 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. Also note that, while the term "Scott domain" is widely used with this definition, the term "domain" does not have such a general meaning: it may be used to refer to many structures in domain theory and is usually explained before it is used. It should be remarked that the property of being bounded complete is equivalent to the existence of all non-empty infima. en.wikipedia.org /wiki/Scott_domain   (561 words)

Complete Heyting algebra -- Facts, Info, and Encyclopedia article   (Site not responding. Last check: 2007-11-07) This article give various characterizations for the notion of a complete Heyting algebra and explains in which sense the notions of a complete Heyting algebra, a locale and a frame differ, although they describe the same mathematical objects. Thus, a homomorphism of complete Heyting algebras is a morphism of frames that in addition preserves implication. Usually the different names for complete Heyting algebras are employed to distinguish these three notions of a morphism implicitly. www.absoluteastronomy.com /encyclopedia/c/co/complete_Heyting_algebra.htm   (758 words)

Complete Complete bipartite graph In vertices can be divided into two non-empty groups, A and B. Each vertex in A is connected to... Complete contract A complete contract is an important concept from contract theory. Complete Heyting algebra In pointless topology, which indeed might roughly be described as the study of locales. www.brainyencyclopedia.com /topics/complete.html   (500 words)

CBD - Concise Bounded Description   (Site not responding. Last check: 2007-11-07) This document [1] defines a concise bounded description of a resource in terms of an RDF graph, as a general and broadly optimal unit of specific knowledge about that resource to be utilized by, and/or interchanged between, semantic web agents. This document defines a concise bounded description of a resource in terms of an RDF graph [5], as a general and broadly optimal unit of specific knowledge about that resource to be utilized by, and/or interchanged between, semantic web agents. Concise bounded descriptions of resources can be considered to be a form of representation, however they are a highly specialized form and not the most usual or obvious form in a web primarily intended for human consumption. swdev.nokia.com /uriqa/CBD.html   (3477 words)

Metric space - Wikipedia, the free encyclopedia If M is a connected Riemannian manifold, then we can turn M into a metric space by defining the distance of two points as the infimum of the lengths of the paths (continuously differentiable curves) connecting them. We call such a subset complete, bounded, totally bounded or compact if it, considered as a metric space, has the corresponding property. A simple way to construct a function separating a point from a closed set (as required for a completely regular space) is to consider the distance between the point and the set. www.bucyrus.us /project/wikipedia/index.php/Metric_space   (1472 words)

BOUNDED - Definition   (Site not responding. Last check: 2007-11-07) bounded interval, boundedly complete, boundedness, bounden, bounder, bounderish In domain theory, a subset S of a cpo X is bounded if there exists x in X such that for all s in S, s <= x. In other words, there is some element above all of S. If every bounded subset of X has a least upper bound then X is boundedly complete. www.hyperdictionary.com /computing/bounded   (63 words)

Completeness Order Theory   (Site not responding. Last check: 2007-11-07) For this reason, posets with certain completeness properties can often be described as algebraic structures of a certain kind. It turns out that in many cases it is possible to characterize completeness solely by considering appropriate algebraic structures in the sense of universal algebra, which are equipped with operations like The considerations in this section suggest a reformulation of (parts of) order theory in terms of category theory, where properties are usually expressed by referring to the relationsships (morphisms, more specifically: adjunctions) between objects, instead of considering their internal structure. www.wikiverse.org /completeness-order-theory   (1833 words)

Completeness (order theory) - InformationBlast The motivation for considering completeness properties derives from the great importance of suprema (least upper bounds, joins, "v") and infima (greatest lower bounds, meets, "^") to the theory of partial orders. The posets with this property are the complete lattices. Consequently, bounded completeness is equivalent to the existence of all non-empty infima. www.informationblast.com /Completeness_%28order_theory%29.html   (1073 words)

wikien.info: Main_Page   (Site not responding. Last check: 2007-11-07) For instance, the completion of a metric space M involves an isometry from M into M', a quotient of the space Cauchy sequences on M. The original space M is thus isometrically isomorphic to a subspace of a complete metric space, and it is usually identified with this subspace. Other embedding constructions show that every metric space is isometrically isomorphic to a closed subset of some normed vector space and that every complete metric space is isometrically isomorphic to a closed subset of some Banach space. pardus.info /index.php?title=Metric_space   (1652 words)

Encyclopedia: Complete partial order   (Site not responding. Last check: 2007-11-07) In mathematics, especially in order theory, the greatest element of a subset S of a partially ordered set is an element of S which is greater than or equal to any other element of S. The term least element is defined dually. In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted by Pop. This is a glossary of some terms used in various branches of mathematics that are related to the fields of order, lattice, and domain theory. www.nationmaster.com /encyclopedia/Complete-partial-order   (1244 words)

english Bounded domains which are universal for minimal surfaces (with W. Complete nonorientable minimal surfaces in a ball (with F.J. López and Santiago Morales). On the asymptotic behavior of a complete bounded minimal surface in R^3 (with S. Morales). www.ugr.es /~fmartin/english_1.htm   (254 words)

[No title]   (Site not responding. Last check: 2007-11-07) Thanks for enlightening me. Keep in mind that "bounded" only makes sense in a metric space, and that "closed" implies X is a subset of something else (evey topological space is closed in itself). R is complete but not the open interval (0,1) to which it is homeomorphic). Date: 28 Jan 1995 19:28:26 GMT A metric space is compact iff it is complete and totally bounded. www.math.niu.edu /~rusin/known-math/95/compact.nss   (1036 words)

Metric space - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-11-07) A metric d on M is called intrinsic if any two points x and y in M can be joint by a curve with length arbitrarily close to d(x, y). A metric space M is called bounded if there exists some number r > 0 such that d(x,y) ≤ r for all x and y in M (not to be confused with "finite", which refers to the number of elements, not to how far the set extends; finiteness implies boundedness, but not conversely). Every complete metric space is isometrically isomorphic to a closed subset of some Banach space. xahlee.org /_p/wiki/Metric_spaces.html   (1390 words)

[No title]   (Site not responding. Last check: 2007-11-07) If X is not totally bounded, there is some e>0 such that no finite collection of balls of radius e covers X. So I can pick x1 in X, x2 in X-B(x1,e), x3 in X - B(x1,e) - B(x2,e), and so on. In somewhat fancier language, call a metric space \emph{totally bounded} if for every given real number $\varepsilon > 0$ it has a finite covering by $\varepsilon$-balls; then, as is easily seen, it is precompact if and only if it is totally bounded. According to the standard characterization of compactness stated above $X$ cannot be totally bounded since it is assumed to be noncompact. www.math.niu.edu /~rusin/known-math/99/cpt_metric   (1381 words)

Bounded Truth-Table and Conjunctive Reductions to Sparse and Tally Sets - Arvind, Kobler, Mundhenk (ResearchIndex)   (Site not responding. Last check: 2007-11-07) Relatedly, we show that if an NP-complete set is bounded-truth-table reducible to a set that co-rp reduces to some set that conjunctively reduces to a sparse set then RP = NP. 0.3: Upper bounds for the Complexity of Sparse and Tally.. Arvind, J. Kobler, M. Mundhenk, "Bounded truth-table and conjunctive reductions to sparse and tally sets," Technical Report, Universit at Ulm Fakultat fur Informatik, 92-01 (April, 1992), 1-22. citeseer.ist.psu.edu /arvind92bounded.html   (787 words)

\bf The Duality Between Aglebraic Posets and Bialgebraic Frames: A Lattice Theoretic Perspective Recall that a complete lattice is said to be coherent provided it is order-isomorphic to the ideal completion of a bounded, distributive lattice. P is order-isomorphic to the prime spectrum of a bounded, distributive lattice in which every element is the join of a finite set of join-prime elements. P is order-isomorphic to the prime spectrum of a bounded, relatively normal lattice in which every element is the join of a finite set of join-prime elements. www.mtsu.edu /~jhart/ALGFRM.html   (9751 words)

Encyclopedia: Bounded complete   (Site not responding. Last check: 2007-11-07) Updated 261 days 4 hours 45 minutes ago. Formally, a partially ordered set (P, ≤) is bounded complete if the following holds for any subset S of P: Click for other authoritative sources for this topic (summarised at Factbites.com). www.nationmaster.com /encyclopedia/Bounded-complete   (469 words)

Poset Properties of Complex Traces   (Site not responding. Last check: 2007-11-07) We show that a subset of G admits a least upper bound if and only if this set is coherent and countable. The compact and the prime dependence graphs are characterized and we prove that each dependence graph is the least upper bound of its compact (resp. We show that C with each order is a coherently complete CPO and we characterize the least upper bound (the greatest lower bound resp.) of a subset of C when it exists. www.liafa.jussieu.fr /~gastin/Articles/Mfcs92gp.html   (161 words)

Bounded complete - TheBestLinks.com - Mathematics, Partially ordered set, Upper bound, Least upper bound, ...   (Site not responding. Last check: 2007-11-07) Bounded complete - TheBestLinks.com - Mathematics, Partially ordered set, Upper bound, Least upper bound,... Bounded complete, Mathematics, Partially ordered set, Upper bound, Least upper... You can add this article to your own "watchlist" and receive e-mail notification about all changes in this page. www.thebestlinks.com /Bounded_complete.html   (487 words)

Maybe this Explains the Economic Cycle... best Complete Metric   (Site not responding. Last check: 2007-11-07) For example, the space of real numbers is complete by Dedekind's axiom, whereas the space of rational numbers is not - e... to a subspace of a complete metric space, and it is usually... Complete Metric Space -- from MathWorld Complete Metric Space -- from MathWorld A complete metric space is a metric space in which every Cauchy sequence is convergent. ascot.pl /th/Fourier3/Complete-Metric.htm   (557 words)

Metric space   (Site not responding. Last check: 2007-11-07) A metric space in which every Cauchy sequence has a limit is said to be complete. If M is a connected Riemannian manifold, then we can turn M into a metric space by defining the distance of two points as the infimum of the lengths of the paths (continuously differentible curves) connecting them. The space M is called totally bounded if for every r > 0 there exist finitely many open balls of radius r whose union equals M. usapedia.com /m/metric-space.html   (1196 words)

Bounded Scheduling of Process Networks   (Site not responding. Last check: 2007-11-07) We present a scheduling policy for complete, bounded execution of Kahn process network programs. In a complete execution, the program terminates if and only if all processes block attempting to consume data from empty communication channels. In a bounded execution, the number of data elements buffered in each of the communication channels remains bounded. ptolemy.eecs.berkeley.edu /publications/papers/95/parksThesis   (168 words)

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