Computability
Computability on computable metric spaces
Theoretical Computer Science
Handbook of logic in computer science (vol. 1)
A faithful computational model of the real numbers
Selected papers of the workshop on Topology and completion in semantics
Computability on subsets of Euclidean space I: closed and compact subsets
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
Computability on continuous, lower semi-continuous and upper semi-continuous real functions
Theoretical Computer Science
Computable analysis: an introduction
Computable analysis: an introduction
Topological properties of real number representations
Theoretical Computer Science
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Computability on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
On computably locally compact hausdorff spaces
Mathematical Structures in Computer Science
The space of formal balls and models of quasi-metric spaces
Mathematical Structures in Computer Science
Computability on subsets of locally compact spaces
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
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In computable analysis recursive metric spaces play an important role, since these are, roughly speaking, spaces with computable metric and limit operation. Unfortunately, the concept of a metric space is not powerful enough to capture all interesting phenomena which occur in computable analysis. Some computable objects are naturally considered as elements of asymmetric spaces which are not metrizable. Nevertheless, most of these spaces are T0-spaces with countable bases and thus at least quasi-metrizable. We introduce a definition of recursive quasi-metric spaces in analogy to recursive metric spaces. We show that this concept leads to similar results as in the metric case and we prove that the most important spaces of computable analysis can be naturally considered as recursive quasi-metric spaces. Especially, we discuss some hyper and function spaces.