A comparison of two systems of point-free topology

Authors

  • Rafał Gruszczyński Nicolaus Copernicus University in Toruń, Department of Logic
  • Andrzej Pietruszczak Nicolaus Copernicus University in Toruń, Department of Logic

DOI:

https://doi.org/10.18778/0138-0680.47.3.04

Keywords:

point-free topology, region-based topology, foundations of topology, mereology, mereological structures, separation structures, connection structures, Grzegorczyk structures, Biacino-Gerla structures.

Abstract

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.

References

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R. Gruszczyński and A. Pietruszczak, A study in Grzegorczyk pointfree topology. Part II: Spaces of points, Studia Logica (2018).
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A. Pietruszczak, Metamereology, Nicolaus Copernicus University Scientific Publishing House, Toruń, 2018.
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Published

2018-10-30

How to Cite

Gruszczyński, R., & Pietruszczak, A. (2018). A comparison of two systems of point-free topology. Bulletin of the Section of Logic, 47(3), 187–200. https://doi.org/10.18778/0138-0680.47.3.04

Issue

Vol. 47 No. 3 (2018)

Section

Research Article

License

Copyright (c) 2018 Bulletin of the Section of Logic

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

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