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).
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