RW-spaces and compactness of function spaces for L-domains

The purpose of this paper is to study the Lawson compactness of function spaces for L-domains. A basic notion of property RW for core compact spaces is introduced, which is proved to have a close relation to the Lawson compactness of function spaces for continuous L-domains as following: (1) Lawson compact continuous dcpo has property RW (via the Scott topology) and for each continuous L-domain, Lawson compactness is equivalent to property RW; be a continuous dcpo with a least element. Then [X→P] is compact continuous for every core compact space X with property RW iff P is compact continuous L-domain; be a core compact space. Then [X→P] is compact for every compact continuous L-domain P iff X has property RW.