Function spaces from core compact coherent spaces to continuous B-domains

Abstract

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. © 2008 Elsevier B.V. All rights reserved.