Geodesic
A comparison of two systems of point-free topology
Bulletin of the Section of Logic, Tome 47 (2018) no. 3.

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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.
Keywords: point-free topology, region-based topology, foundations of topology, mereology, mereological structures, separation structures, connection structures, Grzegorczyk structures, Biacino-Gerla structures. 
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     author = {Gruszczy\'nski, Rafa{\l} and Pietruszczak, Andrzej},
     title = {A comparison of two systems of point-free topology},
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     year = {2018},
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     url = {http://geodesic.mathdoc.fr/item/BSL_2018_47_3_a0/}
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Gruszczyński, Rafał; Pietruszczak, Andrzej. A comparison of two systems of point-free topology. Bulletin of the Section of Logic, Tome 47 (2018) no. 3. http://geodesic.mathdoc.fr/item/BSL_2018_47_3_a0/