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Results tagged with overt-spaces
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user 83901
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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Condition to guarantee that an inhabited and bounded set of reals has a supremum
The following (somewhat strong) property seems to be sufficient:
For any open sets $U,V \subseteq \mathbb{R}$, if $\forall x \in \mathbb{R}.\; x \in U \vee x \in V$, then either $S \subseteq U$ or $S …
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