Compact Locales

A Locale is compact if every Cover has a Finite Subcover.

Like Filtered Categories, one can consider $\kappa$ compact locales for $\kappa$ a Regular Cardinal. In fact, compact locales are precisely the Compact Objects of the Category of Locales.

References

• Picado, Jorge, and Aleš Pultr. Frames and Locales: Topology without Points. Frontiers in Mathematics. Basel: Springer Basel, 2012. https://doi.org/10.1007/978-3-0348-0154-6.