Is the exponential function computable? Are union and intersection of closed subsets of the
real plane computable? Are differentiation and integration computable operators? Is zero …

We present a survey of the recent applications of continuous domains for providing simple
computational models for classical spaces in mathematics including the real line, countably …

Given a partial metric space (X, p), we use (BX,⊑ dp) to denote the poset of formal balls of
the associated quasi-metric space (X, dp). We obtain characterisations of complete partial …

In this dissertation, I explore aspects of computable analysis and topology in the framework
of relative realizability. The computational models are partial combinatory algebras with …

In recent years, there has been a considerable amount of work on using continuous
domains in real analysis. Most notably are the development of the generalized Riemann …

We characterise those quasi-metric spaces (X, d) whose poset BX of formal balls satisfies
the condition (*) From this characterisation, we then deduce that a quasi-metric space (X, d) …

Correctness of algorithms in computational geometry are usually proved using the
unrealistic Real RAM machine model of computation with the undes: uable result that correct …

Based on standard notions of classical recursion theory, a natural model of approximate
computability for partial functions between effective metric spaces is presented. It …

Although there is a somewhat standard formalization of computability on countable sets
given by Turing machines, the same cannot be said about uncountable sets. Among the …

We introduce a partial order⊑ M on the set BX of formal balls of a fuzzy metric space (X,
M,∧) in the sense of Kramosil and Michalek, and discuss some of its properties. We also …