Abstract
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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