Quasiexact posets and the moderate meet-continuity

TL;DR

This paper introduces quasiexact posets and explores their relationships with quasicontinuous domains and weak domains, establishing new connections and properties in domain theory.

Contribution

It defines the weak way-below relation for subsets, introduces quasiexact posets, and studies their topological and order-theoretic properties, linking them to existing domain concepts.

Findings

Quasiexact posets are connected to quasicontinuous and weak domains.

A dcpo is a domain if it is quasiexact and moderately meet continuous.

The weak way-below topology relates to Scott and Mushburn's topologies.

Abstract

The study of weak domains and quasicontinuous domains leads to the consideration of two types generalizations of domains. In the current paper, we define the weak way-below relation between two nonempty subsets of a poset and quasiexact posets. We prove some connections among quasiexact posets, quasicontinuous domains and weak domains. Furthermore, we introduce the weak way-below finitely determined topology and study its links to Scott topology and the weak way-below topology first considered by Mushburn. It is also proved that a dcpo is a domain if it is quasiexact and moderately meet continuous with the weak way-below relation weakly increasing.