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}
}
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

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