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locale; power locale; Hofmann-Mislove theorem; closed subgroup; compact locale; fitted sublocale; categorical logic
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.
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