Posets having continuous intervals

Authors:
Jimmie D. Lawson;Luoshan Xu
Affiliations:
Department of Mathematics, Louisiana State University, Baton Rouge, LA;Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China
Venue:
Theoretical Computer Science - Logic, semantics and theory of programming
Year:
2004

Citing 2
Cited 2

Domain theory

Handbook of logic in computer science (vol. 3)
Dualities of domains

Dualities of domains

Formal topological characterizations of various continuous domains

Computers & Mathematics with Applications
Meet continuity properties of posets

Theoretical Computer Science

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Abstract

In this paper we consider posets in which each order interval [a, b] is a continuous poset or continuous domain. After developing some basic theory for such posets, we derive our major result: if X is a core compact space and L is a poset equipped with the Scott topology (assumed to satisfy a mild extra condition) for which each interval is a continuous sup-semilattice, then the function space of continuous locally bounded functions from X into L has intervals that are continuous sup-semilattices. This substantially generalizes known results for continuous domains.