TY - JOUR AU - Maietti, Maria Emilia AU - Sambin, Giovanni PY - 2013/06/12 Y2 - 2024/03/28 TI - Why topology in the minimalist foundation must be pointfree JF - Logic and Logical Philosophy JA - LLP VL - 22 IS - 2 SE - Articles DO - 10.12775/LLP.2013.010 UR - https://apcz.umk.pl/LLP/article/view/LLP.2013.010 SP - 167–199 AB - <div><p>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 <span style="font-size: 10px;">compulsory. The main reason is that in our foundation real numbers, either as Dedekind cuts or as Cauchy sequences, do not form a set.</span></p></div> ER -