Abstract:Given an axiomatic account of the category of locales the closed subgroup theorem is proved. The theorem is seen as a consequence of a categorical account of the Hofmann-Mislove theorem. The categorical account has an order dual providing a new result for locale theory: every compact subgroup is necessarily fitted.
Keywords: locale, power locale, Hofmann-Mislove theorem, closed subgroup, compact locale, fitted sublocale, categorical logic
AMS Subject Classification: 06D22, 06D50, 54B20, 54B30, 18B30, 18B40