JUCS - Journal of Universal Computer Science 11(12): 2179-2191, doi: 10.3217/jucs-011-12-2179
Sequential Computability of a Function. Effective Fine Space and Limiting Recursion
expand article infoMariko Yasugi, Yoshiki Tsujii, Takakazu Mori§
‡ Kyoto Sangyo University, Kyoto, Japan§ Faculty of Science, Kyoto Sangyo University, Kyoto, Japan
Open Access
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.
Effective Fine Space, Weakly Fine-computable Sequence, Fine-sequential Computability of a Function, Effective Fine-continuous Function, Limiting Recursion