Computability on computable metric spaces
نویسندگان
چکیده
منابع مشابه
Local Computability of Computable Metric Spaces and Computability of Co-c.e. Continua
We investigate conditions on a computable metric space under which each co-computably enumerable set satisfying certain topological properties must be computable. We examine the notion of local computability and show that the result by which in a computable metric space which has the effective covering property and compact closed balls each co-c.e. circularly chainable continuum which is not ch...
متن کاملComputational Complexity on Computable Metric Spaces
We introduce a new Turing machine based concept of time complexity for functions on computable metric spaces. It generalizes the ordinary complexity of word functions and the complexity of real functions studied by Ko [19] et al. Although this definition of TIME as the maximum of a generally infinite family of numbers looks straightforward, at first glance, examples for which this maximum exist...
متن کاملEffective Dispersion in Computable Metric Spaces
We investigate the relationship between computable metric spaces (X, d, α) and (X, d, β), where (X, d) is a given metric space. In the case of Euclidean space, α and β are equivalent up to isometry, which does not hold in general. We introduce the notion of effectively dispersed metric space. This notion is essential in the proof of the main result of this paper: (X, d, α) is effectively totall...
متن کاملEffective zero-dimensionality for computable metric spaces
We begin to study classical dimension theory from the computable analysis (TTE) point of view. For computable metric spaces, several effectivisations of zerodimensionality are shown to be equivalent. The part of this characterisation that concerns covering dimension extends to higher dimensions and to closed shrinkings of finite open covers. To deal with zero-dimensional subspaces uniformly, fo...
متن کاملComputability of semicomputable manifolds in computable topological spaces
We study computable topological spaces and semicomputable and computable sets in these spaces. In particular, we investigate conditions under which semicomputable sets are computable. We prove that a semicomputable compact manifold M is computable if its boundary ∂M is computable. We also show how this result combined with certain construction which compactifies a semicomputable set leads to th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 1993
ISSN: 0304-3975
DOI: 10.1016/0304-3975(93)90001-a