Why topology in the minimalist foundation must be pointfree

Maria Emilia Maietti, Giovanni Sambin

DOI: http://dx.doi.org/10.12775/LLP.2013.010

Abstract


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.


Keywords


pointfree topology; real numbers; choice sequences’ Bar Induction; constructive type theory; axiom of unique choice; minimalist foundation

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