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Investigation of topological spaces using relators

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Investigation of topological spaces using relators

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dc.contributor.author Pataki, Gergely es_ES
dc.date.accessioned 2022-05-25T07:02:36Z
dc.date.available 2022-05-25T07:02:36Z
dc.date.issued 2022-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/182880
dc.description.abstract [EN] In this paper, we define uniformities and topologies as relators and show the equivalences of these definitions with the classical ones. For this, we summarize the essential properties of relators, using their theory from earlier works of Á. Száz.Moreover, we prove implications between important topological properties of relators and disprove others. Finally, we show that our earlier analogous definition [G. Pataki, Investigation of proximal spaces using relators, Axioms 10, no. 3 (2021): 143.] for uniformly and proximally filtered property is equivalent to the topological one.At the end of this paper, uniformities and topologies are defined in the same way. This will give us new possibilities to compare these and other topological structures. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València es_ES
dc.relation.ispartof Applied General Topology es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject (generalized) uniformities es_ES
dc.subject (generalized) topologies es_ES
dc.subject Relators es_ES
dc.title Investigation of topological spaces using relators es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2022.16128
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Pataki, G. (2022). Investigation of topological spaces using relators. Applied General Topology. 23(1):45-54. https://doi.org/10.4995/agt.2022.16128 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2022.16128 es_ES
dc.description.upvformatpinicio 45 es_ES
dc.description.upvformatpfin 54 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 23 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\16128 es_ES
dc.description.references N. Bourbaki, Topologie Générale, Herman, Paris (1953). es_ES
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dc.description.references G. Pataki, On the extensions, refinements and modifications of relators, Math. Balk. 15 (2001), 155-186. es_ES
dc.description.references G. Pataki, Investigation of proximal spaces using relators, Axioms 10, no. 3 (2021): 143. es_ES
dc.description.references https://doi.org/10.3390/axioms10030143 es_ES
dc.description.references G. Pataki and A. Száz, A unified treatment of well-chainedness and connectedness properties, Acta Math. Acad. Paedagog. Nyházi. (N.S.) 19 (2003), 101-166. es_ES
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dc.description.references https://doi.org/10.1007/BF01440953 es_ES
dc.description.references Á. Száz, Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50 (1987), 177-201. es_ES
dc.description.references https://doi.org/10.1007/BF01903935 es_ES
dc.description.references Á. Száz, Directed, topological and transitive relators, Publ. Math. Debrecen 35 (1988), 179-196. es_ES
dc.description.references Á. Száz, Relators, Nets and Integrals, Unfinished Doctoral Thesis (1991). es_ES
dc.description.references A. Weil, Sur les espaces a structure uniforme at sur la topologie générale, Actualités Sci. Ind. 551, Herman and Cie, Paris, 1937. es_ES


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