The Continuous Functionals of Finite Types Over the Reals
Dag Normann · Electronic Notes in Theoretical Computer Science · 2000
We investigate the hierarchy of functionals of finite types over the reals based on a standard domain representation of R. We prove that for each type, the total functionals are dense in the set of partial functionals. Moreover we give a characterisation of the functionals of each type in terms of limit spaces, and we prove a general lifting theorem for each of these types.