Banach Spaces as Data Types
نویسنده
چکیده
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.
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عنوان ژورنال:
- Logical Methods in Computer Science
دوره 7 شماره
صفحات -
تاریخ انتشار 2011