Mostrar el registro sencillo del ítem
dc.contributor.author | Jäger, Gunther![]() |
es_ES |
dc.date.accessioned | 2023-05-02T07:07:38Z | |
dc.date.available | 2023-05-02T07:07:38Z | |
dc.date.issued | 2023-04-05 | |
dc.identifier.issn | 1576-9402 | |
dc.identifier.uri | http://hdl.handle.net/10251/193028 | |
dc.description.abstract | [EN] Based on the concept of Cauchy pair Τ-filters, we develop an axiomatic theory of completeness for non-symmetric spaces, such as Τ-quasi-uniform (limit) spaces or L-metric spaces. We show that the category of Τ-quasi-Cauchy spaces is topological and Cartesian closed and we construct a finest completion for a non-complete Τ-quasi-Cauchy space. In the special case of symmetry, Τ-quasi-Cauchy spaces can be identified with Τ-Cauchy spaces. | 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 | Fuzzy topology | es_ES |
dc.subject | L-metric space | es_ES |
dc.subject | Pair T-filter | es_ES |
dc.subject | Cuachy pair T-filter | es_ES |
dc.subject | T-quasi-Cauchy space | es_ES |
dc.subject | T-quasi-uniform space | es_ES |
dc.title | Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion | es_ES |
dc.type | Artículo | es_ES |
dc.identifier.doi | 10.4995/agt.2023.18783 | |
dc.rights.accessRights | Abierto | es_ES |
dc.description.bibliographicCitation | Jäger, G. (2023). Τ-quasi-Cauchy spaces - a non-symmetric theory of completeness and completion. Applied General Topology. 24(1):205-227. https://doi.org/10.4995/agt.2023.18783 | es_ES |
dc.description.accrualMethod | OJS | es_ES |
dc.relation.publisherversion | https://doi.org/10.4995/agt.2023.18783 | es_ES |
dc.description.upvformatpinicio | 205 | es_ES |
dc.description.upvformatpfin | 227 | 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\18783 | es_ES |
dc.description.references | J. J. Adámek, H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989. | es_ES |
dc.description.references | R. Bĕlohlávek, Fuzzy Relation Systems, Foundation and Principles, Kluwer Academic/Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2002. | es_ES |
dc.description.references | M. M. Clementino and D. Hofmann, Lawvere completeness in topology, Appl. Categ. Struct. 17 (2009), 175-210. https://doi.org/10.1007/s10485-008-9152-5 | es_ES |
dc.description.references | D. Doitchinov, Completeness in quasi-metric spaces, Topology Appl. 30 (1988), 127-148. https://doi.org/10.1016/0166-8641(88)90012-0 | 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 | W. F. Lindgren and P. Fletcher, A construction of the pair completion of a quasi-uniform space, Can. Math. Bull. 21 (1978), 53-59. https://doi.org/10.4153/CMB-1978-009-2 | es_ES |
dc.description.references | J. Gutiérrez-García, On stratified L-valued filters induced by Τ-filters, Fuzzy Sets and Systems 157 (2006), 813-819. https://doi.org/10.1016/j.fss.2005.09.003 | es_ES |
dc.description.references | J. He, H. Lai and L. Shen, Towards probabilistic partial metric spaces: Diagonals between distance distributions, Fuzzy Sets and Systems 370 (2019), 99-119. https://doi.org/10.1016/j.fss.2018.07.011 | es_ES |
dc.description.references | U. Höhle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Math. 38 (1982), 289-323. https://doi.org/10.1007/BF01170928 | 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), 53-106. https://doi.org/10.1007/978-94-011-0215-5_5 | es_ES |
dc.description.references | D. Hofmann and W. Tholen, Lawvere Completion and separation via closure, Appl. Categ. Struct. 18 (2010), 259-287. https://doi.org/10.1007/s10485-008-9169-9 | es_ES |
dc.description.references | D. Hofmann, G. J. Seal and W. Tholen, Monoidal topology, Cambridge University Press 2014. https://doi.org/10.1017/CBO9781107517288 | es_ES |
dc.description.references | G. Jäger and Y. Yue, Τ-uniform convergence spaces, Iranian J. Fuzzy Syst. 19, no. 2 (2022), 133-149. | es_ES |
dc.description.references | G. Jäger, Diagonal conditions and uniformly continuous extension in Τ-uniform limit spaces, Iranian J. Fuzzy Syst. 19, no. 5 (2022), 131-145. | es_ES |
dc.description.references | G. Jäger, Sequential completeness for Τ-quasi-uniform spaces and a fixed point theorem, Mathematics 10 (2022): 2285. https://doi.org/10.3390/math10132285 | es_ES |
dc.description.references | H. H. Keller, Die Limes-Uniformisierbarkeit der Limesräume, Math. Annal. 176 (1968), 334-341. https://doi.org/10.1007/BF02052894 | es_ES |
dc.description.references | H. P. A. Künzi, An introduction to quasi-uniform spaces, in: Beyond Topology, F. Mynard, E. Pearl, eds., Contempory Mathematics 486, Amer. Math. Soc., Providence, Rhodes Island (2009), 239-304. https://doi.org/10.1090/conm/486/09511 | 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 | G. Preuβ, Prefilter spaces and a precompletion of preuniform convergence spaces related to some well-known completions, Topology Appl. 156 (2009), 2005 - 2012. https://doi.org/10.1016/j.topol.2009.03.026 | es_ES |
dc.description.references | E. E. Reed, Completion of uniform convergence spaces, Math. Annal. 194 (1971), 83-108. https://doi.org/10.1007/BF01362537 | es_ES |
dc.description.references | L. Reid and G. Richardson, Lattice-valued spaces: Τ-completions, Fuzzy Sets and Systems 369 (2019), 1-19. https://doi.org/10.1016/j.fss.2018.06.003 | es_ES |
dc.description.references | B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North Holland, New York, 1983. | es_ES |
dc.description.references | Y. Wang and Y. Yue, Cauchy completion of fuzzy quasi-uniform Spaces, Filomat 35, no. 12 (2021), 3983-4004. https://doi.org/10.2298/FIL2112983W | es_ES |
dc.description.references | Q. Yu and J. Fang, The category of Τ-convergence spaces and its cartesian-closedness, Iranian J. of Fuzzy Systems 14, no. 3 (2017), 121-138. | es_ES |
dc.description.references | Y. Yue and J. Fang, Completeness in probabilistic quasi-uniform spaces, Fuzzy Sets and Systems 370 (2019), 34-62. https://doi.org/10.1016/j.fss.2018.08.005 | es_ES |
dc.description.references | D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems 158 (2007), 349-366. https://doi.org/10.1016/j.fss.2006.10.001 | es_ES |