WHY TOPOLOGY IN THE MINIMALIST FOUNDATION MUST BE POINTFREE. - Maietti, Maria Emilia; Sambin, Giovanni (Logic & Logical Philosophy, 2013)
We give arguments explaining why, when adopting a minimalist approach to constructive mathematics as that formalized in our two-level minimalist foundation, the choice for a pointfree approach to topology is not just a matter of convenience or mathematical elegance, but becomes compulsory. The main reason is that in our foundation real numbers, either as Dedekind cuts or as Cauchy sequences, do not form a set.