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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).
4
votes
A topological concept dual to compactness
It suffices to consider the $T_0$ spaces as other cases can be handled by replicating points.
Let $X$ be an "anti-compact" $T_0$ space. It is worthwhile to look at the specialization order on the poin …