Irreducible locales


Dharmanand Baboolal, Paranjothi Pillay




Basic properties of irreducible locales which extend results contained in [4] are presented. Our main result is that every locale L can be embedded as a closed nowhere dense sublocale of an irreducible localeIL, what we call the irreducible envelope of L. The properties of spatiality, subfitness, fitness, compactness, and the Noetherian property are shown to be inherited and reflected by the irreducible envelope