The regular-locally compact coreflection of a stably locally compact locale

The Scott continuous nuclei form a subframe of the frame of all nuclei. We refer to this subframe as the patch frame. We show that the patch construct ion exhibits (i) the category of regular locally compact locales and perfec t maps as a coreflective subcategory of the category of stably locally comp act locales and perfect maps, (ii) the category of compact regular locales and continuous maps as a coreflective subcategory of the category of stably compact locales and perfect maps, and (iii) the category of Stone locales and continuous maps as a coreflective subcategory of the category of spectr al locales and perfect maps. (Here a stably locally compact locale is not n ecessarily compact, and a stably compact locale is a compact and stably loc ally compact locale.) We relate our patch construction to Banaschewski and Brummer's construction of the dual equivalence of the category of stably co mpact locales and perfect maps with the category of compact regular biframe s and biframe homomorphisms. (C) 2001 Elsevier Science B.V. All rights rese rved. MSC: 06B35; 06E15; 54A10; 54H10.