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Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

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Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems

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dc.contributor.author Peters, James Francis es_ES
dc.contributor.author Vergili, Tane es_ES
dc.date.accessioned 2023-04-26T11:41:53Z
dc.date.available 2023-04-26T11:41:53Z
dc.date.issued 2023-04-05
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/192968
dc.description.abstract [EN] This paper introduces proximal path cycles, which lead to the main results in this paper, namely, extensions of the Mitsuishi-Yamaguchi Good Coverning Theorem with different forms of Tanaka good cover of an Alexandrov space equipped with a proximity relation as well as extension of the Jordan curve theorem. In this work, a path cycle is a sequence of maps h1,...,hi,...,hn-1 mod n in which hi  : [ 0,1 ] ? X and hi(1) = hi+1(0) provide the structure of a path-connected cycle that has no end path. An application of these results is also given for the persistence of proximal video frame shapes that appear in path cycles. es_ES
dc.description.sponsorship The first author has been supported by the Natural Sciences & Engineering Research Council of Canada (NSERC) discovery grant 185986 and Instituto Nazionale di Alta Matematica (INdAM) Francesco Severi, Gruppo Nazionale per le Strutture Algebriche, Geometriche e Loro Applicazioni grant 9 920160 000362, n.prot U 2016/000036 and Scientific and Technological Research Council of Turkey (TUBITAK) Scientific Human Resources Development (BIDEB) under grant no: 2221-1059B211301223. 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 Cycle es_ES
dc.subject Good cover es_ES
dc.subject Homotopy es_ES
dc.subject Nerve es_ES
dc.subject Path es_ES
dc.subject Proximity es_ES
dc.title Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2023.17046
dc.relation.projectID info:eu-repo/grantAgreement/TUBITAK//2221-1059B211301223 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSERC//185986 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GNSAGA//9 920160 000362 es_ES
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Peters, JF.; Vergili, T. (2023). Good coverings of proximal Alexandrov spaces. Path cycles in the extension of the Mitsuishi-Yamaguchi good covering and Jordan Curve Theorems. Applied General Topology. 24(1):25-45. https://doi.org/10.4995/agt.2023.17046 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2023.17046 es_ES
dc.description.upvformatpinicio 25 es_ES
dc.description.upvformatpfin 45 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 24 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\17046 es_ES
dc.contributor.funder Natural Sciences and Engineering Research Council of Canada es_ES
dc.contributor.funder Scientific and Technological Research Council of Turkey es_ES
dc.contributor.funder Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni es_ES
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