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Topic: Scott-continuous

    Note: these results are not from the primary (high quality) database.

[XMATdb5r%DDATHD21.BITNET@MITVMA.MIT.EDU: Note for the TYPES mailing lis The proof is based on the following crucial LEMMA: Let D and E be algebraic dcpo's with property m such that the space [D ---> E] of Scott-continuous functions is algebraic. In their recent paper "Domain Theoretic Models of Polymorphism", which will appear shortly in Information and Computation, Coquand, Gunter and Winskel (CGW) show how to use the class S of all (countably based) Scott-domains as a model for the polymorphic lambda calculus. Since F is continuous, any continuous section of F is determined by its values on the finite posets contained in C. There are only set-many finite posets up to isomorphism, so we can study the set \Pi F = {(t_X)_{X\in C_fin} www.seas.upenn.edu /~sweirich/types/archive/1988/msg00097.html   (783 words)

\bf The Duality Between Aglebraic Posets and Bialgebraic Frames: A Lattice Theoretic Perspective D] is the set of all Scott continuous maps from C to D under the pointwise ordering.) The formation of finite cartesian products and function spaces both have natural meanings as type constructors - processes by which new types may be constructed from existing ones. Q is Scott continuous provided f preserves directed joins. The domains are assigned a topology based upon their ordering, known as the Scott topology, the open sets of which represent the formulas specifying programs. www.mtsu.edu /~jhart/ALGFRM.html   (783 words)

Barendregt: Lambda Calculus The tree topology on an open or closed term model M is the largest topology making the map taking lambda-terms to their equivalence classes continuous (where the lambda-terms have the tree topology given by Bohm terms). The Scott topology on X is the same as the subspace topology (since the ordering and the sup's are the same). [Scott 1980] C(A) is a CCC with reflexive object I with arrows F=G=1. www.andrew.cmu.edu /user/cebrown/notes/barendregt.html   (783 words)

Topology Seminar If X and Y are locales, then the natural transformations from $^X to $^Y are in bijection with the Scott continuous functions from the frame of X to the frame of Y, which were already known to be in bijection with the maps from Y to PP(X). Then the basic deal in semantics is that a domain, with its Scott topology, embodies a logical theory of how one can observe some type of program by watching it run (without access to the source code). A space X is called exponentiable if such a suitable topology exists on the set continuous maps from X to Y for every space Y. It is well-known that a Hausdorff space is exponentiable if and only if it is locally compact, and that in this case the exponential topology is the compact-open topology. www.cs.bham.ac.uk /research/events/topology-seminar/topology.html   (783 words)

eWiC: VDM meets LCF: Domain-Theoretic and Topological Aspects of VDM Indeed, the strong Cantor topology is the smallest topology which refines the Scott and Lawson topologies and is such that, with respect to it, all the basic operators we consider are continuous. It turns out that the override, one of the more important of the basic operators, is not Scott continuous, and in order to overcome this problem we introduce another topology, which we call here the strong Cantor topology, by means of the topological tool of convergence classes. Furthermore, we examine the role of the strong Cantor topology in relation to indexed monoids, both with and without units, and display them as topological monoids in the strong Cantor topology. ewic.bcs.org /conferences/2001/5thformal/papers/paper6.htm   (783 words)

Tomasz Kubiak For L a meet-continuous lattice with \gamma (L) weaker than the Scott topology of L, this is the case if and only if \hfill\break (*) \qquad \alpha=\sup{\beta in L : \alpha in Int There is an easy argument showing that every completely distributive lattice L with \gamma (L) stronger than the upper topology satisfies the condition (\star), which thus provides a short proof that each completely distributive lattice is hypercontinuous (hence continuous). Topology Atlas Conference Abstracts Document # caah-59.htm www.utm.edu /~jschomme/topology/c/a/a/h/59.htm   (783 words)

Scott Topology Following [ 12 ] we prove that in the case of a continuous lattice $\langle C,\ \leq \rangle$ the Scott convergence is topological, i.e. We formalize the theorem, that if the Scott convergence has the (ITERATED LIMITS) property, the $\langle C,\ \leq \rangle$ is continuous. When $\langle C,\ \leq \rangle$ is a complete lattice we say that $L$ is Scott, if $\tau$ is the Scott topology of $\langle C,\ \leq \rangle$. megrez2.mizar.org /mirror/JFM/Vol9/waybel11.html   (783 words)

Continuous Integration on Hanselminutes Scott Hanselman has posted a new episode of his Hanselminutes podcast dedicated to continuous integration. In the podcast Scott had a brainstorm and forgot the name of Sean McCormack's unit testing tool Zanebug. At the moment this is the best place to find news, updates and help using the add-in. weblogs.asp.net /nunitaddin/archive/2006/02/01/437051.aspx   (208 words)

Michael Bukatin - Papers in Computer Science My co-author Joshua Scott received his undergraduate degree in Math from Brandeis (Spring 1996) and now studies at Northeastern. The paper introduces a new notion of co-continuity for valuations and shows how to build continuous partial and relaxed metrics from co-continuous valuations on domains. This electronic version of 06/19/00 is the same as the text published in the proceedings of 14th Summer Conference on General Topology and its Applications. www.cs.brandeis.edu /~bukatin/papers.html   (208 words)

Scott is Phoa, locally In a paper circulated since end of last year Dana Scott has proposed a category PEQU of algebraic lattices with partial equivalence relations as objects and equivariant Scott continuous maps as morphisms. One nice thing about PEQU is that Scott has shown it to be equivalent to the category EQU of T_0 spaces with (total) equivalence relations and equivariant continuous maps. It has been shown (by students of Scott) that PEQU is not even well-powered despite being regular and locally cartesian closed (in particular, it is a logos and thus a model for FOL). www.cis.upenn.edu /~bcpierce/types/archives/1997-98/msg00098.html   (402 words)

ENGLISH PAGE - Continuous Conditionals Past Unreal Conditional + Continuous is used to discuss imaginary situations happening at a very specific time in the past or over a period of time in the past. Future Unreal Conditional + Continuous can be used like the Future Continuous in imaginary situations to emphasize interruptions or parallel actions in the future. Past Unreal Conditional + Continuous can be used like the Past Continuous in imaginary situations to emphasize interruptions or parallel actions in the past. www.englishpage.com /conditional/continuousconditional.html   (920 words)

Grainger Museum - Cyril Scott Cyril Scott's return to England around the turn of the century marked the beginning of a long and fruitful career as a composer at the forefront of English modernism. Cyril Scott's extraordinarily diverse range of interests were reflected in his writings. Scott's 1904 publishing agreement with Elkin and Co resulted in widespread recognition for many of these smaller works, and made Scott an internationally known name. www.lib.unimelb.edu.au /collections/grainger/percy/cyril.html   (500 words)

Encyclopedia: Alexandrov topology Notice however that in the case of topologies other than the Alexandrov topology, we can have a map between two topological spaces that is not continuous but which is nevertheless still a monotone function between the corresponding preordered sets. With the advancement of categorical topology in the 1980s, Alexandrov spaces were rediscovered when the concept of finite generation was applied to general topology and the name finitely generated spaces was adopted for them. Inspired by the use of Alexandrov topologies in computer science, applied mathematicians and physicists in the late 1990's began investigating the Alexandrov topology corresponding to causal sets which arise from a preorder defined on spacetime modeling causality. www.nationmaster.com /encyclopedia/Alexandrov-topology   (500 words)

Order theory - Wikipedia, the free encyclopedia Gierz, K. Hofmann, K. Keimel, J. Lawson, M. Mislove, and D. Scott, Continuous Lattices and Domains, In Encyclopedia of Mathematics and its Applications, Vol. The finest order consistent topology is the Scott topology, which is coarser than the Alexandrov topology. Beyond these relations, topology can be looked at solely in terms of the open set lattices, which leads to the study of pointless topology. en.wikipedia.org /wiki/Order_theory   (500 words)

The Calgary Sun - Brison busted Brison stated, both on national television while in the lobby of the House of Commons and in his written press release, that as NCC president, "Harper made continuous representations to public office holders on many different issues. However, the plan's one major flaw was inadvertently displayed, not by the Conservatives, but by Liberal Scott Brison, the minister of public works and government services. Brison's press release announced he has asked the Office of the Registrar of Lobbyists to investigate Harper, saying Harper "was in contravention of the Lobbyist Registration Act when he was president of the NCC for four years between 1997 and 2001." calsun.canoe.ca /News/Columnists/Corbella_Licia/2005/11/08/1297079.html   (643 words)

Freddie Mac News Archive:  Rep. Scott, Freddie Mac, H.O.M.E. City of Richmond, Launch "Virginia Lending Protection Project" Uniting Anti-Predatory Lending Drive With Safe, Flexible Mortgages for Homeownership. Freddie Mac is a stockholder-owned corporation established by Congress in 1970 to create a continuous flow of funds to mortgage lenders in support of homeownership and rental housing. "Homeownership is a critical building block for Virginia families working to achieve the American dream," said Congressman Robert C. "Bobby” Scott. Freddie Mac purchases mortgages from lenders and packages them into securities that are sold to investors. www.freddiemac.com /news/archives/predatory_lending/2004/richmond_032604.html   (798 words)

Topology in Computer Science Complete lattices as fixed points of Scott continuous transformations of powersets. A basis for the Scott topology on X is given by B = { A, B, C, D where A = { a,b,c,d }, B = { b,d }, C = { c,d }, and D = { d }. Ever since domains were introduced by Dana Scott [Sco70] and Yuri Ershov [Ers75], a question in the centre of interest was to find suitable cartesian closed categories of domains and the quest for cartesian closed categories as large as possible, so to be closed under various domain-theoretic constructions. www.informatik.uni-siegen.de /theo/TopCS.html   (798 words)

Quantitative Domain Theory In this framework, the least fixed point of a functional, defined on a domain of Scott continuous functions and with range in the same set, is obtained as a topological limit. The topology involved is now known as the Scott topology. Scott’s work quickly led to connections with the mathematical fields of Topology and Category Theory. www.ercim.org /publication/Ercim_News/enw50/schellekens.html   (798 words)

PRG Research Report RR-03-07 Moreover, the space ker μ in its relative Scott topology is homeomorphic to the Vietoris hyperspace of ker &mu, i.e., the space of nonempty compact subsets of ker &mu in its Vietoris topology -- the topology induced by any Hausdorff metric. We show that a measurement &mu on a continuous dcpo D extends to a measurement μ on the convex powerdomain C D iff it is a Lebesgue measurement. In particular, ker &mu must be metrizable in its relative Scott topology. web.comlab.ox.ac.uk /oucl/publications/tr/rr-03-07.html   (798 words)

oe magazine - eye on technology Scott Diddams of NIST discussed his "clock-work" using femtosecond titanium-doped sapphire lasers and photonic crystal fibers to produce a comb of frequencies, in which each tooth of the comb is a sharp, spectrally pure frequency spaced by some time interval. One tooth of the comb is locked to the frequency of a continuous-wave laser, which in turn is locked to the atomic clock transition such that the repetition rate of the femtosecond laser can be made an exact sub-multiple of the frequency of the probe laser. A high-frequency optical oscillator is important, but it is equally as important to faithfully count each and every optical cycle, which comes at a rate of 500 THz. oemagazine.com /fromTheMagazine/apr03/eyeontech.html   (798 words)

Poppyland Clement Scott's Poppy-land consisted of the area between Cromer and Mundesley, but the railways, who used Poppy-land as an advertisement for their train services to the east coast, and other writers who wrote about the area, enlarged Poppy-land to take in Sheringham on one side, and almost as far as Yarmouth on the other. CLEMENT SCOTT looked down on this summer scene of Cromer and its sands from Lighthouse Hill, a mile to the east. When Clement Scott first called at the miller's house, and the pretty nineteen-year-old Louie opened the door, perhaps he fell in love with her as well. stanfield.und.ac.za /poppy02.html   (798 words)

Quantitative Domain Theory In this framework, the least fixed point of a functional, defined on a domain of Scott continuous functions and with range in the same set, is obtained as a topological limit. Domain Theory, a formal basis for the semantics of programming languages, originated in work by Dana Scott in the mid-1960s. Scott’s work quickly led to connections with the mathematical fields of Topology and Category Theory. www.ercim.org /publication/Ercim_News/enw50/schellekens.html   (702 words)

Speech Transcript - Eric Rudder, Professional Developers Conference - 2003 Some will actually take on the burden, like Scott showed you in the user management system, but there are areas probably where we can all benefit from a little bit more defensive layers using encryption or other techniques to kind of increase the security that we provide. It turns out you're not going to have to worry about that with "Whitehorse,", Eric, because in "Whitehorse,", the designers are actually in the implementation are kept in continuous synchronization. Now, you'll notice I'm logged in as Scott onto the site, there's now a personalize link that's showing up here. www.microsoft.com /presspass/exec/ericr/10-28pdc2003.asp   (702 words)

sepcont Every continuous dcpo with its Scott topology satisfies condition (2) with F being a singleton. No non-discrete T_1 topology is possible; any order topology has the property and we have at least one other space and that about exhausts our knowledge of the subject. To prove 1 => 2, let Y be the space of open sets of X, where the topology is generated by assuming all neighborhood filters of points of X as open. www.mta.ca /~cat-dist/catlist/1999/sepcont   (216 words)

Scott is Phoa, locally In a paper circulated since end of last year Dana Scott has proposed a category PEQU of algebraic lattices with partial equivalence relations as objects and equivariant Scott continuous maps as morphisms. One nice thing about PEQU is that Scott has shown it to be equivalent to the category EQU of T_0 spaces with (total) equivalence relations and equivariant continuous maps. x R y } and the pair e,p of equivariant Scott continuous maps establishes an isomorphism between (L,R) and (P $\omega$, e[R]). www.cis.upenn.edu /~bcpierce/types/archives/1997-98/msg00098.html   (402 words)

ejmcexample.tex This paper provides a quasi-metric topology for the interval space consistent with the real line topology and whose continuous function are exactly the monotonic ones. In \cite{Aci91} was defined on the set of intervals a topology- the Scott topology-where this viewpoint is suported. A {\em topology} on a set $X$ is a collection of subsets of $X$ which is closed under finite intersections and arbitrary unions, including the empty set and the set $X$ itself. gmc.ucpel.tche.br /ejmc/ejmcexample.tex   (402 words)

Topologies on Spaces of Continuous Functions (Abstract) We show that the intersection of the approximating topologies of any preframe is the Scott topology. The only prerequisite to this development is a basic knowledge of general topology (continuous functions, product topology and compactness). In particular, we conclude that a complete lattice is continuous if and only if it has a smallest approximating topology and finite meets distribute over directed joins. rw4.cs.uni-sb.de /~heckmann/abstracts/topfunc.html   (402 words)

CSP25 - Order, topology, and recursion induction in CSP University of Oxford, UK Abstract: Recursion induction is a method for proving that CSP processes which are defined as the least fixed points of some Scott-continuous function from a complete partial order on the set of all processes to itself meet a given behavioural specification. The Scott (order version) requires that (1) the specification S is closed via the least upper bound of directed sets in the complete partial order, (2) S(bottom), and (3) if S(P) then S(F(P). In this talk we develop a general theory for recursion induction based on the Scott topology of the maximal elements in a domain. www.lsbu.ac.uk /menass/csp25/programme/csp25mr.html   (402 words)

Abbas Edalat The set of probability distributions on this dcpo can be ordered to give another \omega -continuous dcpo called the probabilistic power domain of the upper space. The crucial point is that the set of probability distributions on the metric space, equipped with the weak topology, can be embedded into the set of maximal elements of the probabilistic power domain. Suppose we have a probability distribution on a compact metric space, given by its value on a countable base, and suppose we have a real-valued Lipschitz function on the space. www.utm.edu /~jschomme/topology/c/a/a/e/18.htm   (402 words)

CEOL Home Then each topology arises from such a generalized metric and for each continuous poset there is such a generalized metric whose topology is the Scott topology and whose dual topology is the lower topology. Next we study their completion and show that for every auxiliary relation on a poset there is join preserving partial metric such that round ideal completion is the spherically completion. We generalize this notion to study ``partial metrics" whose values lie in a value lattice which may be other than the reals. www.ceol.ucc.ie /index_files/seminars.htm   (402 words)

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