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
Mariko Yasugi‡, Yoshiki Tsujii‡, Takakazu Mori§‡ Kyoto Sangyo University, Kyoto, Japan§ Faculty of Science, Kyoto Sangyo University, Kyoto, Japan
Corresponding author: Mariko Yasugi ( yasugi@cc.kyoto-su.ac.jp ) © Mariko Yasugi, Yoshiki Tsujii, Takakazu Mori. This article is freely available under the J.UCS Open Content License. Citation:
Yasugi M, Tsujii Y, Mori T (2005) Sequential Computability of a Function. Effective Fine Space and Limiting Recursion. JUCS - Journal of Universal Computer Science 11(12): 2179-2191. https://doi.org/10.3217/jucs-011-12-2179 |  |
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, Weakly Fine-computable Sequence, Fine-sequential Computability of a Function, Effective Fine-continuous Function, Limiting Recursion