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...
| Publicado en: | Logic & Logical Philosophy Vol. 22; no. 2; pp. 167 - 200 |
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| Autores principales: | , |
| Formato: | Artículo |
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Logic & Logical Philosophy
Jun2013
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=88839410&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 88839410 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 14253305 DS9 jtl: Logic & Logical Philosophy issn: 14253305 maglogo: N pubinfo: dt: Jun2013 vid: 22 iid: 2 pid: 42904 pub: Logic & Logical Philosophy artinfo: ui: 88839410 10.12775/LLP.2013.010 ppf: 167 ppct: 33 formats: fmt: @attributes: type: P size: 1.6MB tig: atl: WHY TOPOLOGY IN THE MINIMALIST FOUNDATION MUST BE POINTFREE. aug: au: Maietti, Maria Emilia Sambin, Giovanni affil: Dipartimento di Matematica, Università di Padova, via Trieste 63 35121 Padova, Italy su: Mathematical programming Mathematics Topology Real numbers Axioms sug: subj: Mathematical programming Mathematics Topology Real numbers Axioms keyword: axiom of unique choice Bar Induction choice sequences constructive type theory minimalist foundation pointfree topology real numbers ab: 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. pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Copyright of Logic & Logical Philosophy is the property of Logic & Logical Philosophy and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. item: Logic & Logical Philosophy holder: Logic & Logical Philosophy dt: @attributes: year: 2013 holdings: @attributes: islocal: N |
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