Categories, types, and structures: an introduction to category theory for the working computer scientist
Computable analysis: an introduction
Computable analysis: an introduction
Theoretical Computer Science
Comparing Functional Paradigms for Exact Real-Number Computation
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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The compact-open topology on the set of continuous functionals from the Baire space to the natural numbers is well known to be zero-dimensional. We prove that the closely related sequential topology on this set is not even regular. The sequential topology arises naturally as the topology carried by the exponential formed in various cartesian closed categories of topological spaces. Moreover, we give an example of an effectively open subset of that violates regularity. The topological properties of are known to be closely related to an open problem in Computable Analysis. We also show that the sequential topology on the space of continuous real-valued functions on a Polish space need not be regular.