Description

• Title:
  A comparison of two systems of point-free topology
• Creator:
  Gruszczyński, Rafał;
  Pietruszczak, Andrzej
• Contributor:
  Nicolaus Copernicus University in Toruń, Department of Logic;
  gruszka@umk.pl;
  pietrusz@umk.pl
• Description:
  This is a spin-off paper to [3, 4] in which we carried out an extensive analysis of Andrzej Grzegorczyk’s point-free topology from [5]. In [1] Loredana Biacino and Giangiacomo Gerla presented an axiomatization which was inspired by the Grzegorczyk’s system, and which is its variation. Our aim is to compare the two approaches and show that they are slightly different. Except for pointing to dissimilarities, we also demonstrate that the theories coincide (in the sense that their axioms are satisfied in the same class of structures) in presence of axiom stipulating non-existence of atoms.
• Object availability:
  free access
• Rights:
  This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.;
  http://creativecommons.org/licenses/by-nc-nd/4.0
• Date:
  2019.04.26;
  2018
• Type:
  Article
• Language:
  English
• Format:
  application/pdf
• Publisher:
  Wydawnictwo Uniwersytetu Łódzkiego
• Relation:
  Bulletin of the Section of Logic; 3;
  47
• Subject:
  point-free topology;
  region-based topology;
  foundations of topology;
  mereology;
  mereological structures;
  separation structures;
  connection structures;
  Grzegorczyk structures;
  Biacino-Gerla structures.
• Identifier:
  0138-0680;
  http://hdl.handle.net/11089/28052 ;
  2449-836X;
  10.18778/0138-0680.47.3.04
• Data provider:
  Repozytorium Uniwersytetu Łódzkiego
• Can I use it?:
  check license
• Type:
  image