COMPUTABLY COMPACT METRIC SPACES
Rodney G. Downey, Alexander Melnikov
Abstract
Abstract We give a systematic technical exposition of the foundations of the theory of computably compact metric spaces. We discover several new characterizations of computable compactness and apply these characterizations to prove new results in computable analysis and effective topology. We also apply the technique of computable compactness to give new and less combinatorially involved proofs of known results from the literature. Some of these results do not have computable compactness or compact spaces in their statements, and thus these applications are not necessarily direct or expected.
Topics & Concepts
Compact spaceMathematicsMathematical proofMetric spaceMetric (unit)Exposition (narrative)Computable analysisAlgebra over a fieldDiscrete mathematicsComputable functionPure mathematicsTopology (electrical circuits)CombinatoricsLiteratureGeometryOperations managementEconomicsArtComputability, Logic, AI AlgorithmsAdvanced Topology and Set TheoryMathematical and Theoretical Analysis