Coincidence of the Isbell and Scott topologies on domain function spaces

Let [X→L] be the set of all continuous mappings from a topological space X to a domain L with the pointwise order. Let Is[X→L], σ[X→L] be the Isbell and Scott topologies on [X→L] respectively. In this paper, the question of when the Isbell and Scott topologies coincide on [X→L] is considered. Main results are: