The Equivalence of QRB, QFS, and Compactness for Quasicontinuous Domains

In this article we show the equivalence of QRB, QFS, and compact quasicontinuous domains. QRB and QFS domains are generalizations of RB and FS domains to the setting of quasicontinuous domains and compactness means compactness in the Lawson topology. This equivalence extends in the algebraic setting to a quasicontinuous version of bifinite domains. The Smyth powerdomain is a basic tool in the proofs, and it is shown that quasicontinuous properties at the dcpo level typically have the corresponding continuous domain properties at the Smyth powerdomain level.