Computability on computable metric spaces
Theoretical Computer Science
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 on subsets of metric spaces
Theoretical Computer Science - Topology in computer science
Computable Riesz Representation for the Dual of C [0;1]
Electronic Notes in Theoretical Computer Science (ENTCS)
Computable Riesz Representation for Locally Compact Hausdorff Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
Effectivity on Continuous Functions in Topological Spaces
Electronic Notes in Theoretical Computer Science (ENTCS)
On computably locally compact hausdorff 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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By Dini’s theorem on a compact metric space K any increasing sequence (gi)i∈ℕ of real-valued continuous functions converging pointwise to a continuous function f converges uniformly. In this article we prove a fully computable version of a generalization: a modulus of uniform convergence can be computed from a quasi-compact subset K of a computable T0-space with computable intersection, from an increasing sequence of lower semi-continuous real-valued functions on K and from an upper semi-continuous function to which the sequence converges. For formulating and proving we apply the representation approach to Computable Analysis (TTE) [1]. In particular, for the spaces of quasi-compact subsets and of the partial semi-continuous functions we use natural multi-representations [2]. Moreover, the operator computing a modulus of convergence is multi-valued.