Why Topology in the Minimalist Foundation Must be Pointfree

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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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10.12775/llp.2013.010

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References found in this work

Constructive Analysis.Errett Bishop & Douglas Bridges - 1987 - Journal of Symbolic Logic 52 (4):1047-1048.
Inductively generated formal topologies.Thierry Coquand, Giovanni Sambin, Jan Smith & Silvio Valentini - 2003 - Annals of Pure and Applied Logic 124 (1-3):71-106.

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