Computable analysis: an introduction
Computable analysis: an introduction
Admissible Representations of Limit Spaces
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
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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.