Computably Compact Metric Spaces

Bulletin of Symbolic Logic 29 (2):170-263 (2023)
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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.



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Computable Stone spaces.Nikolay Bazhenov, Matthew Harrison-Trainor & Alexander Melnikov - 2023 - Annals of Pure and Applied Logic 174 (9):103304.

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