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Overtness is the lattice dual of compactness in various forms of constructive topology and analysis, where related ideas are also called "located" (constructive analysis), "recursively enumerable" (computable analysis), "open" (locale theory) or "positive" (formal topology).
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What does overtness mean for metric spaces?
In computable analysis, the typical approach to metric spaces is that of a computable metric space. If we assume that there already is some external concept of the metric space we want to handle, we w …