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The Continuous Functionals of Finite Types Over the Reals

Authors
Journal
Electronic Notes in Theoretical Computer Science
1571-0661
Publisher
Elsevier
Publication Date
Volume
35
Identifiers
DOI: 10.1016/s1571-0661(05)80738-8
Disciplines
  • Mathematics

Abstract

Abstract 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.

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