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# Locatedness and overt sublocales

@article{Spitters2010LocatednessAO, title={Locatedness and overt sublocales}, author={Bas Spitters}, journal={Ann. Pure Appl. Logic}, year={2010}, volume={162}, pages={36-54} }

- Published 2010 in Ann. Pure Appl. Logic
DOI:10.1016/j.apal.2010.07.002

Locatedness is one of the fundamental notions in constructive mathematics. The existence of a positivity predicate on a locale, i.e. the locale being overt, or open, has proved to be fundamental in constructive locale theory. We show that the two notions are intimately connected. Bishop defines a metric space to be compact if it is complete and totally bounded. A subset of a totally bounded set is again totally bounded iff it is located. So a closed subset of a Bishop compact set is Bishop… CONTINUE READING