Sequential Computability of a Function. Effective Fine Space and Limiting Recursion
Mariko Yasugi (Faculty of Science, Kyoto Sangyo University, Japan)
Yoshiki Tsujii (Faculty of Science, Kyoto Sangyo University, Japan)
Takakazu Mori (Faculty of Science, Kyoto Sangyo University, Japan)
Abstract: We consider real sequences in I = [0, 1) and real functions on I. It is first shown that, as for real sequences from I, R-computability (computability with respect to the Euclidean topology) implies “ weak Fine-computability.” Using this result, we show that “ Finesequential computability” and “ -sequential computability” are equivalent for effectively locally Fine-continuous functions as well as for Fine-continuous functions.
Keywords: Effective Fine Space, Effective Fine-continuous Function, Fine-sequential Computability of a Function, Limiting Recursion, Weakly Fine-computable Sequence
Categories: F.0, G.0