Sequential Computability of a Function: Diagonal Space and Limiting Recursion

Tsujii, Yoshiki; Yasugi, Mariko; Mori, Takakazu

doi:10.1016/j.entcs.2004.06.044

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“…A similar notion of computability for functions on effective uniform topological spaces can be found in [9]. In [10], these three computabilities on the Fine metric space are generalized to effective uniform topological spaces. But they have not been compared with Type-2 computability.…”

Section: Introductionmentioning

confidence: 96%

Effective continuities on effective topological spaces

Iizuka

2006

Journal of Complexity

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We extend a notion of effective continuity due to Mori, Tsujii and Yasugi to real-valued functions on effective topological spaces. Under reasonable assumptions, Type-2 computability of these functions is characterized as sequential computability and the effective continuity. We investigate effective uniform topological spaces with a separating set, and adapt the above result under some assumptions. It is also proved that effective local uniform continuity implies effective continuity under the same assumptions.

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Section: Introductionmentioning

confidence: 96%