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  1. 1 Logic and Logical Philosophy

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  1. 1 Maietti M. E.

  2. 1 Sambin G.

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  1. 1 2013

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Why Topology in the Minimalist Foundation Must be Pointfree

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Maietti M. E., Sambin G.
Logic and Logical Philosophy
|
2013
|
vol. 22
|
issue 2
167-199
EN
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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