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A comparison of two systems of point-free topology

dc.contributor.authorGruszczyński, Rafał
dc.contributor.authorPietruszczak, Andrzej
dc.date.accessioned2019-04-26T14:21:43Z
dc.date.available2019-04-26T14:21:43Z
dc.date.issued2018
dc.identifier.issn0138-0680
dc.identifier.urihttp://hdl.handle.net/11089/28052
dc.description.abstractThis 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.en_GB
dc.language.isoenen_GB
dc.publisherWydawnictwo Uniwersytetu Łódzkiegoen_GB
dc.relation.ispartofseriesBulletin of the Section of Logic; 3
dc.rightsThis work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.en_GB
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0en_GB
dc.subjectpoint-free topologyen_GB
dc.subjectregion-based topologyen_GB
dc.subjectfoundations of topologyen_GB
dc.subjectmereologyen_GB
dc.subjectmereological structuresen_GB
dc.subjectseparation structuresen_GB
dc.subjectconnection structuresen_GB
dc.subjectGrzegorczyk structuresen_GB
dc.subjectBiacino-Gerla structures.en_GB
dc.titleA comparison of two systems of point-free topologyen_GB
dc.typeArticleen_GB
dc.page.number187-200
dc.contributor.authorAffiliationNicolaus Copernicus University in Toruń, Department of Logic
dc.contributor.authorAffiliationNicolaus Copernicus University in Toruń, Department of Logic
dc.identifier.eissn2449-836X
dc.references[1] L. Biacino and G. Gerla, Connection structures: Grzegorczyk’s and Whitehead’s definitions of point, Notre Dame Journal of Formal Logic 37 (3) (1996), pp. 431–439. http://dx.doi.org/10.1305/ndjfl/1039886519.en_GB
dc.references[2] R. Gruszczy´nski and A. Pietruszczak, Space, points and mereology. On foundations of point-free Euclidean geometry. Logic and Logical Philosophy 18 (2) (2009), pp. 145–188. http://dx.doi.org/10.12775/LLP.2009.009.en_GB
dc.references[3] R. Gruszczy´nski and A. Pietruszczak, A study in Grzegorczyk point-free topology. Part I: Separation and Grzegorczyk structures, Studia Logica, Vol. 106 (2018), pp. 1197–1238. https://doi.org/10.1007/s11225-018-9786-8.en_GB
dc.references[4] R. Gruszczy´nski and A. Pietruszczak, A study in Grzegorczyk pointfree topology. Part II: Spaces of points, Studia Logica (2018). https://doi.org/10.1007/s11225-018-9822-8.en_GB
dc.references[5] A. Grzegorczyk, Axiomatizability of geometry without points, Synthese 12 (2–3) (1960), pp. 228–235. DOI: http://dx.doi.org/10.1007/BF00485101.en_GB
dc.references[6] A. Pietruszczak, Metamereology, Nicolaus Copernicus University Scientific Publishing Hause, Toru´n, 2018. DOI: http://dx.doi.org/10.12775/9751.en_GB
dc.contributor.authorEmailgruszka@umk.pl
dc.contributor.authorEmailpietrusz@umk.pl
dc.identifier.doi10.18778/0138-0680.47.3.04
dc.relation.volume47en_GB


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