Why topology in the minimalist foundation must be pointfree
Keywordspointfree topology, real numbers, choice sequences’ Bar Induction, constructive type theory, axiom of unique choice, minimalist foundation
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.
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