Domains with Approximating Projections
نویسنده
چکیده
We investigate approximating posets with projections (approximating pop's). These are triples (D; ; P) consisting of a poset (D;) and a directed set P of projections with sup P = id D. They carry a canonical uniformity and thus a topology. We relate their properties such as completeness and compactness to properties of the poset and the projection set. We show that each monotone net in D is convergent if and only if (D;) is an algebraic domain such that the images of the projections are precisely the compact elements of (D;). We call these domains P-domains and characterize them as inverse limits of posets satisfying the ascending chain condition. Moreover, we describe P-domains by a certain system of so-called \complete" subsets. We prove that if the set of compact elements of an algebraic domain is mub-complete, then it is a P-domain if and only if the mub-closure of every nite set of compact elements fullls the ascending chain condition. Furthermore, we characterize biinite domains both as compact approximating pop's and as P-domains in which nite sets of compact elements have nite complete sets of minimal upper bounds.
منابع مشابه
Very Sparse Stable Random Projections, Estimators and Tail Bounds for Stable Random Projections
The method of stable random projections [39, 41] is popular for data streaming computations, data mining, and machine learning. For example, in data streaming, stable random projections offer a unified, efficient, and elegant methodology for approximating the lα norm of a single data stream, or the lα distance between a pair of streams, for any 0 < α ≤ 2. [18] and [20] applied stable random pro...
متن کاملContinuity results with respect to domain perturbation for the fractional p-Laplacian
In this paper we give sufficient conditions on the approximating domains in order to obtain the continuity of solutions for the fractional p−laplacian. These conditions are given in terms of the fractional capacity of the approximating domains.
متن کاملLevel of Grammatical Proficiency and Acquisition of Functional Projections: The case of Iranian learners of English language
Unlike Lexical Projections, Functional Projections (Extended Projections) are more of an ‘abstract’ in nature. Therefore, Functional Projections seem to be acquired later than Lexical Projections by the L2 learners. The present study investigates Iranian L2 learners’ acquisition of English Extended Projections taking into account their level of grammatical proficiency. Specifically, the aim is ...
متن کاملGalerkin domain decomposition procedures for parabolic equations on rectangular domain
Galerkin domain decomposition procedures for parabolic equations with three cases of boundary conditions on rectangular domain are discussed. These procedures are non-iterative and non-overlapping ones. They rely on implicit Galerkin method in the sub-domains and integral mean method on the inter-domain boundaries to present explicit flux calculation. Thus, the parallelism can be achieved by th...
متن کامل