Abstract
We investigate a hierarchy of domains with totality where we close some selected base domains, including domains for the reals, the natural numbers and the boolean values, under cartesian products and restricted function spaces. We show that the total objects will be dense in the respective domains, and that our construction is equivalent to the analogue construction in the category of limit spaces.
In order to obtain this we will consider a restricted function space construction. We then show that this restriction, up to equivalence, does not restrict the class of total objects.
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Normann, D. (2001). The Continuous Functionals of Finite Types Over the Reals. In: Keimel, K., Zhang, GQ., Liu, YM., Chen, YX. (eds) Domains and Processes. Semantic Structures in Computation, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-0654-5_6
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DOI: https://doi.org/10.1007/978-94-010-0654-5_6
Publisher Name: Springer, Dordrecht
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