- -

Quantale-valued Cauchy tower spaces and completeness

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Quantale-valued Cauchy tower spaces and completeness

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: JagerAhsanullah - ...
Tamaño: 302.4Kb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Jäger, Gunther es_ES
dc.contributor.author Ahsanullah, T. M. G. es_ES
dc.date.accessioned 2021-10-06T07:47:36Z
dc.date.available 2021-10-06T07:47:36Z
dc.date.issued 2021-10-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/173929
dc.description.abstract [EN] Generalizing the concept of a probabilistic Cauchy space, we introduce quantale-valued Cauchy tower spaces. These spaces encompass quantale-valued metric spaces, quantale-valued uniform (convergence) tower spaces and quantale-valued convergence tower groups. For special choices of the quantale, classical and probabilistic metric spaces are covered and probabilistic and approach Cauchy spaces arise. We also study completeness and completion in this setting and establish a connection to the Cauchy completeness of a quantale-valued metric space. 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 Cauchy space es_ES
dc.subject Quantale-valued metric space es_ES
dc.subject Quantale-valued uniform convergence tower space es_ES
dc.subject Completeness es_ES
dc.subject Completion es_ES
dc.subject Cauchy completeness es_ES
dc.title Quantale-valued Cauchy tower spaces and completeness es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2021.15610
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Jäger, G.; Ahsanullah, TMG. (2021). Quantale-valued Cauchy tower spaces and completeness. Applied General Topology. 22(2):461-481. https://doi.org/10.4995/agt.2021.15610 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2021.15610 es_ES
dc.description.upvformatpinicio 461 es_ES
dc.description.upvformatpfin 481 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 22 es_ES
dc.description.issue 2 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\15610 es_ES
dc.description.references J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989. es_ES
dc.description.references T. M. G. Ahsanullah and G. Jäger, Probabilistic uniform convergence spaces redefined, Acta Math. Hungarica 146 (2015), 376-390. https://doi.org/10.1007/s10474-015-0525-6 es_ES
dc.description.references T. M. G. Ahsanullah and G. Jäger, Probabilistic uniformization and probabilistic metrization of probabilistic convergence groups, Math Slovaca 67 (2017), 985-1000. https://doi.org/10.1515/ms-2017-0027 es_ES
dc.description.references P. Brock and D. C. Kent, Approach spaces, limit tower spaces, and probabilistic convergence spaces, Appl. Cat. Structures 5 (1997), 99-110. https://doi.org/10.1023/A:1008633124960 es_ES
dc.description.references H. R. Fischer, Limesräume, Math. Ann. 137 (1959), 269-303. https://doi.org/10.1007/BF01360965 es_ES
dc.description.references R. C. Flagg, Completeness in continuity spaces, in: Category Theory 1991, CMS Conf. Proc. 13 (1992), 183-199. es_ES
dc.description.references R. C. Flagg, Quantales and continuity spaces, Algebra Univers. 37 (1997), 257-276. https://doi.org/10.1007/s000120050018 es_ES
dc.description.references L. C. Florescu, Probabilistic convergence structures, Aequationes Math. 38 (1989), 123-145. https://doi.org/10.1007/BF01839999 es_ES
dc.description.references G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous lattices and domains, Cambridge University Press, 2003. https://doi.org/10.1017/CBO9780511542725 es_ES
dc.description.references D. Hofmann and C. D. Reis, Probabilistic metric spaces as enriched categories, Fuzzy Sets and Systems 210 (2013), 1-21. https://doi.org/10.1016/j.fss.2012.05.005 es_ES
dc.description.references U. Höhle, Commutative, residuated l-monoids, in: Non-classical logics and their applications to fuzzy subsets (U. Höhle, E. P. Klement, eds.), Kluwer, Dordrecht 1995, pp. 53-106. https://doi.org/10.1007/978-94-011-0215-5_5 es_ES
dc.description.references G. Jäger, A convergence theory for probabilistic metric spaces, Quaest. Math. 38 (2015), 587-599. https://doi.org/10.2989/16073606.2014.981734 es_ES
dc.description.references G. Jäger and T. M. G. Ahsanullah, Probabilistic limit groups under a $t$-norm, Topology Proceedings 44 (2014), 59-74. es_ES
dc.description.references G. Jäger and T. M. G. Ahsanullah, Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence, Applied Gen. Topology 19, no. 1 (2018), 129-144. https://doi.org/10.4995/agt.2018.7849 es_ES
dc.description.references G. Jäger, Quantale-valued uniform convergence towers for quantale-valued metric spaces, Hacettepe J. Math. Stat. 48, no. 5 (2019), 1443-1453. https://doi.org/10.15672/HJMS.2018.585 es_ES
dc.description.references G. Jäger, The Wijsman structure of a quantale-valued metric space, Iranian J. Fuzzy Systems 17, no. 1 (2020), 171-184. es_ES
dc.description.references H. H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Ann. 176 (1968), 334-341. https://doi.org/10.1007/BF02052894 es_ES
dc.description.references D. C. Kent and G. D. Richardson, Completions of probabilistic Cauchy spaces, Math. Japonica 48, no. 3 (1998), 399-407. es_ES
dc.description.references F. W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matematico e Fisico di Milano 43 (1973), 135-166. Reprinted in: Reprints in Theory and Applications of Categories} 1 (2002), 1-37. https://doi.org/10.1007/BF02924844 es_ES
dc.description.references R. Lowen, Index Analysis, Springer, London, Heidelberg, New York, Dordrecht 2015. https://doi.org/10.1007/978-1-4471-6485-2 es_ES
dc.description.references R. Lowen and Y. J. Lee, Approach theory in merotopic, Cauchy and convergence spaces. I, Acta Math. Hungarica 83, no. 3 (1999), 189-207. https://doi.org/10.1023/A:1006717022079 es_ES
dc.description.references R. Lowen and Y. J. Lee, Approach theory in merotopic, Cauchy and convergence spaces. II, Acta Math. Hungarica 83, no. 3 (1999), 209-229. https://doi.org/10.1023/A:1006769006149 es_ES
dc.description.references R. Lowen and B. Windels, On the quantification of uniform properties, Comment. Math. Univ. Carolin. 38, no. 4 (1997), 749-759. es_ES
dc.description.references R. Lowen and B. Windels, Approach groups, Rocky Mountain J. Math. 30, no. 3 (2000), 1057-1073. https://doi.org/10.1216/rmjm/1021477259 es_ES
dc.description.references J. Minkler, G. Minkler and G. Richardson, Subcategories of filter tower spaces, Appl. Categ. Structures 9 (2001), 369-379. https://doi.org/10.1023/A:1011226611840 es_ES
dc.description.references H. Nusser, A generalization of probabilistic uniform spaces, Appl. Categ. Structures 10 (2002), 81-98. https://doi.org/10.1023/A:1013375301613 es_ES
dc.description.references H. Nusser, Completion of probabilistic uniform limit spaces, Quaest. Math. 26 (2003), 125-140. https://doi.org/10.2989/16073600309486049 es_ES
dc.description.references G. Preuß, Seminuniform convergence spaces, Math. Japonica 41, no. 3 (1995), 465-491. es_ES
dc.description.references G. Preuß, Foundations of topology. An approach to convenient topology, Kluwer Academic Publishers, Dordrecht, 2002. https://doi.org/10.1007/978-94-010-0489-3 es_ES
dc.description.references Q. Pu and D. Zhang, Preordered sets valued in a GL-monoid, Fuzzy Sets and Systems 187 (2012), 1-32. https://doi.org/10.1016/j.fss.2011.06.012 es_ES
dc.description.references G. N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4 (1953), 518-512. https://doi.org/10.1090/S0002-9939-1953-0058568-4 es_ES
dc.description.references E. E. Reed, Completion of uniform convergence spaces, Math. Ann. 194 (1971), 83-108. https://doi.org/10.1007/BF01362537 es_ES
dc.description.references G. D. Richardson and D. C. Kent, Probabilistic convergence spaces, J. Austral. Math. Soc. (Series A) 61 (1996), 400-420. https://doi.org/10.1017/S1446788700000483 es_ES
dc.description.references B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland, New York, 1983. es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem