Description

• Title:
  Why topology in the minimalist foundation must be pointfree
• Creator:
  Maietti, Maria Emilia;
  Sambin, Giovanni
• Description:
  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.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2017 Logic and Logical Philosophy
• Date:
  2013.06.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion
• Language:
  English
• Source:
  Logic and Logical Philosophy; Vol. 22 No. 2 (2013): June; 167–199;
  Logic and Logical Philosophy; Tom 22 Nr 2 (2013): June; 167–199;
  2300-9802;
  1425-3305
• Format:
  application/pdf
• Publisher:
  Uniwersytet Mikołaja Kopernika w Toruniu
• Relation: https://apcz.umk.pl/LLP/article/view/LLP.2013.010/767
• Subject:
  pointfree topology;
  real numbers;
  choice sequences’ Bar Induction;
  constructive type theory;
  axiom of unique choice;
  minimalist foundation;
  MSC 2000;
  03G30 03B15 18C50 03B20 03F55
• Identifier: https://apcz.umk.pl/LLP/article/view/LLP.2013.010
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  text