Continuity of Function Spaces from Pointwise Directed Families of Characteristic Functions

In earlier work the second author introduced the tool of pointwise directed families of characteristic functions to establish that certain continuous function spaces [X → Q] were continuous domains. In this paper we extend those earlier results, while significantly simplifying and refining the machinery involved. Our main result asserts that the function space [X → Q] is a continuous dcpo if X is locally compact and coherent and Q is a retract of a bifinite domain (RB-domain) with ⊥