Why Topology in the Minimalist Foundation Must be Pointfree

Logic and Logical Philosophy 22 (2):167-199 (2013)
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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

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