M-SCOTT CONVERGENCE AND M-SCOTT TOPOLOGY ON POSETS

Quantale-valued fuzzy Scott topology

The aim of this paper is to extend the truth value table oflattice-valued convergence spaces to a more general case andthen to use it to introduce and study the quantale-valued fuzzy Scotttopology in fuzzy domain theory. Let $(L,*,varepsilon)$ be acommutative unital quantale and let $otimes$ be a binary operationon $L$ which is distributive over nonempty subsets. The quadruple$(L,*,otimes,varep...

Topological Scott Convergence Theorem

Recently, J. D. Lawson encouraged the domain theory community to consider the scientific program of developing domain theory in the wider context of T0 spaces instead of restricting to posets. In this paper, we respond to this calling with an attempt to formulate a topological version of the Scott Convergence Theorem, i.e., order-theoretic characterisation of those posets for which the Scott-co...

The Scott Topology . Part II

The following propositions are true: (1) Let X be a set and F be a finite family of subsets of X. Then there exists a finite family G of subsets of X such that G ⊆ F and ⋃ G = ⋃ F and for every subset g of X such that g ∈ G holds g 6⊆ ⋃ (G \ {g}). (2) Let S be a 1-sorted structure and X be a subset of the carrier of S. Then −X = the carrier of S if and only if X is empty. (3) Let R be an antisy...

Louis J . Gross , Scott M . Duke - Sylvester , and Mark Palmer

Toru Suzuki , Scott L . Friedman , Luisa M . Botella and Carmelo Bernabéu Eva M . Garrido - Martín ,

Eva M. Garrido-Martín, Francisco J. Blanco, Mercé Roquè, Laura Novensà, Mirko Tarocchi, Activin Receptor-Like Kinase 1 Gene Specificity Protein 1 to Promote Endothelial Activation Through Upregulation of the Vascular Injury Triggers Krüppel-Like Factor 6 Mobilization and Cooperation With Print ISSN: 0009-7330. Online ISSN: 1524-4571 Copyright © 2012 American Heart Association, Inc. All rights r...