“Predicative theory of stably locally compact locales”
Venerdì 3 Febbraio 2023, ore 15:00 - Aula 1A150 - Tatsuji Kawai (JAIST, Japan)
We give a predicative presentation of stably locally compact locales, the class of locales which includes locally compact regular locales (e.g., localic reals) as its subclass. In our setting, a stably locally compact locale is presented as a quasi-proximity lattice, a quasi-bounded distributive lattice (distributive lattice without top) together with a certain idempotent relation on it. Using this structure, we construct a coreflection from the category of locally compact regular locales and cobounded maps to that of stably locally compact locales and perfect maps. The construction of this coreflection generalizes Dedekind’s construction of real numbers as pairs of a lower and an upper cut.