作为数据类型的巴拿赫空间
Banach Spaces as Data Types
摘要：
我们在巴拿赫空间上引入算子“修正极限”和“累积”，并使用它来定义在空间上内部可计算的含义。证明了从可计算度量空间到可计算巴拿赫空间的任何外可计算函数都是内可计算的。我们的动机需要内部的概念的可计算性观察到的复杂性的有限集的封闭球与非空的交集是不一致的超算术，因此，近似的外部可计算的功能是非常复杂的。
英文摘要：
We introduce the operators "modified limit" and "accumulation" on a Banach space, and we use this to define what we mean by being internally computable over the space. We prove that any externally computable function from a computable metric space to a computable Banach space is internally computable. We motivate the need for internal concepts of computability by observing that the complexity of the set of finite sets of closed balls with a nonempty intersection is not uniformly hyperarithmetical, and thus that approximating an externally computable function is highly complex.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
