Complexity theory of real functions
Complexity theory of real functions
Computability on computable metric spaces
Theoretical Computer Science
Computability on subsets of Euclidean space I: closed and compact subsets
Theoretical Computer Science - Special issue on computability and complexity in analysis
Concrete models of computation for topological algebras
Theoretical Computer Science - Special issue on computability and complexity in analysis
Effective properties of sets and functions in metric spaces with computability structure
Theoretical Computer Science - Special issue on computability and complexity in analysis
Computable analysis: an introduction
Computable analysis: an introduction
Computability theory of generalized functions
Journal of the ACM (JACM)
Theoretical Computer Science - Topology in computer science
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Continuity and computability of reachable sets
Theoretical Computer Science
A computable version of dini's theorem for topological spaces
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
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Locally compact Hausdorff spaces generalise Euclidean spaces and metric spaces from ‘metric’ to ‘topology’. But does the effectivity on the latter (Brattka and Weihrauch 1999; Weihrauch 2000) still hold for the former? In fact, some results will be totally changed. This paper provides a complete investigation of a specific kind of space – computably locally compact Hausdorff spaces. First we characterise this type of effective space, and then study computability on closed and compact subsets of them. We use the framework of the representation approach, TTE, where continuity and computability on finite and infinite sequences of symbols are defined canonically and transferred to abstract sets by means of notations and representations.