QC-continuity of posets and the Hoare powerdomain of QFS-domains

摘要

In terms of Scott-closed sets, the concept of QC-continuous posets, a generalization of C-continuous lattices is introduced. With this new concept, the following results are obtained: (1) a complete lattice is generalized completely distributive (GCD) iff it is quasicontinuous and QC-continuous; (2) a dcpo L is quasicontinuous (resp., quasialgebraic) if the Hoare powerdomain H(L) is quasicontinuous (resp., quasialgebraic); (3) the Hoare powerdomain H(L) of a QFS-domain L is still a QFS-domain. (C) 2015 Elsevier B.V. All rights reserved.