Function Spaces From Core Compact Coherent Spaces To Continuous B-domains

摘要

It is proved in this paper that for a continuous B-domain L, the function space |X→L| is continuous for each core compact and coherent space X. Further, applications are given. It is proved that: (1) the function space from the unit interval to any bifinite domain which is not an L-domain is not Lawson compact; (2) the Isbell and Scott topologies on |X → L| agree for each continuous B-domain L and core compact coherent space X.