Local computability of computable metric spaces and computability of co-c.e. continua

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...

Perfect Local Computability and Computable Simulations

We study perfectly locally computable structures, which are (possibly uncountable) structures S that have highly effective presentations of their local properties. We show that every such S can be simulated, in a strong sense and even over arbitrary finite parameter sets, by a computable structure. We also study the category theory of a perfect cover of S, examining its connections to the categ...

Computability 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...

Computable Functional Analysis and Probabilistic Computability

Models of Computability Incomputability and Oracle Machines Computability and Information Computable Enumerability

What is computability? What does it tell us, and why should we be interested in it? Unlike with more obviously practical topics, we do need to ask such questions before talking about technical aspects. Computability as a field is broadly defined by the work and research interests of Alan Turing, who started out as a mathematician. Its distinctive features are: • A multidisciplinary approach to ...