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WHY TOPOLOGY IN THE MINIMALIST FOUNDATION MUST BE POINTFREE.

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...

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Publicado en:Logic & Logical Philosophy Vol. 22; no. 2; pp. 167 - 200
Autores principales: Maietti, Maria Emilia, Sambin, Giovanni
Formato: Artículo
Publicado: Logic & Logical Philosophy Jun2013
Materias:
Mathematical programming
Mathematics
Topology
Real numbers
Axioms
Acceso en línea:Ver este registro en EBSCOhost
Sumario: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.