Abstract
The upper powerdomain of an arbitrary dcpo L can be constructed by the Scott completion of the directed upper powerspace of L. By means of this result, we investigate the upper powerdomains of quasicontinuous domains. The main results are: (1) The upper powerdomain PU(L) of a quasicontinuous domain L is quasicontinuous iff the directed upper powerspace of L is endowed with the Scott topology, iff PU(L) is isomorphic to Q(L), the semilattice of nonempty Scott compact saturated subsets of L. (2) There exists a quasicontinuous dcpo whose upper powerdomain is not quasicontinuous. (3) The upper powerdomain of a strongly quasicontinuous domain L is isomorphic to Q(L).
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.