Abstract
One standard way of constructing a hierarchy of total, continuous functionals over a fixed set of base types is to use a suitable cartesian closed category of domains where we may construct the corresponding hierarchy of partial continuous functionals, and then extract the hereditarily total ones. One important theorem, when available, is the Density Theorem: Each finitary domain object can be extended to a total one.
We will see how we in the context of limit spaces, may formulate and prove versions of the density theorems and avoid domain theory.
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Normann, D. (2008). Internal Density Theorems for Hierarchies of Continuous Functionals. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_50
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DOI: https://doi.org/10.1007/978-3-540-69407-6_50
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