Abstract:
The heredity, invariance and mapping space of quasicontinuous Domains are discussed. It is proved that quasicontinuous Domains and quasialgebraic Domains are hereditary for scott open subsets and scott closed subsets, and the images of a quasicintinuous domain and a quasialgebraic Domain under the way below-preserving quasi-Scott continuous map are still quasicontinuous and quasialgebraic,respectively. It is shown that if X and L are bounded complete quasicontinuous Domains and L is totally ordered, then the mapping space ［X→Ｌ］ of all Scott continuous maps is a bounded complete quasicontinuous Domain.
