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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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Intermediate value theorem on computable reals
Let me assume that you are speaking about computable reals and functions in the sense of
computable analysis, which is one of the most successful approaches to the topic. (One must be careful, since t …