Computable analysis: an introduction
Computable analysis: an introduction
Representations versus numberings: on the relationship of two computability notions
Theoretical Computer Science
On the computability of Walsh functions
Theoretical Computer Science
Some Properties of the Effective Uniform Topological Space
CCA '00 Selected Papers from the 4th International Workshop on Computability and Complexity in Analysis
Sequential Computability of a Function: Diagonal Space and Limiting Recursion
Electronic Notes in Theoretical Computer Science (ENTCS)
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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.