Abstract
An attempt is made to lay a basis for a general, unified, concise, and simple theory of computable and continuous functions from F to F or N , where F = {f: N → N }. The theoy is formally very similar to ordinary recursion theory. It splits into a purely topological version and more special theory of computability. The basic definitions are given and fundamental properties are proved. As an example it is shown how the theory of recursively enumerable subsets of N can be transferred to a theory of open and a theory of computably open subsets of F .
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