Jimmie Lawson

Directed Complete Completions

Abstract: We introduce a variant of the Scott topology,
called the D-topology.  We consider the D-completion for both
topological spaces and posets and derive its basic properties. For
partially ordered sets the D-completion turns out to be a
natural dcpo-completion that generalizes the rounded ideal
completion.  We establish that various types of continuous
operations extend uniquely continuously to the D-completion, and
thus this completion provides a potentially useful approach to
dcpo-algebras.