algebraic poset

Noun

algebraic poset (plural algebraic posets)

1. A partially ordered set (poset) in which every element is the supremum of the compact elements below it.
   • A poset (P,<) is said to be algebraic if and only if
     i) P is up-complete, i.e., for every non-empty up-directed subset D,thesupremum operatorname supd exists,
     ii) for every x∈P, the set
     K_X:=y∈P|ycompact,y<x
     is non-empty and up-directed, and
     x= operatorname supK_x.
     A poset P is an algebraic poset...1985 October, Rudolf-E. Hoffmann, The Injective Hull and the 𝒞ℒ-Compactification of a Continuous Poset, Canadian Journal of Mathematics, 37:5, Canadian Mathematical Society, page 833
   • ALG is the category whose objects are algebraic posets and whose morphisms are continuous functions.
     A structure (D,#92;le#95;D,#92;cup#95;D) where (D,#92;le#95;D) is an algebraic poset and #92;cup#95;D is a binary operation on D which is continuous (in both variables), commutative, associative and...1988, Karel Hrbacek, “A Powerdomain Construction”, in Michael Main, Austin Melton, Michael Mislove, David Schmidt, editors, Mathematical Foundations of Programming Language Semantics: 3rd Workshop...