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Completeness of L-quasi-uniform convergence spaces | ||
Iranian Journal of Fuzzy Systems | ||
دوره 20، شماره 2، خرداد و تیر 2023، صفحه 57-67 اصل مقاله (190.36 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2023.7556 | ||
نویسندگان | ||
L. Sun؛ Y. Yue* | ||
Department of Mathematics, Ocean University of China, Qingdao, 266100, P. R. China | ||
چکیده | ||
The aim of this paper is to study the completeness of L-quasi-uniform convergence spaces and L-quasi-uniform spaces. Firstly, we describe L-quasi-uniform convergence spaces as enriched categories. Then we give two kinds of completeness of L-quasi-uniform convergence spaces and show that Lawvere completeness implies Cauchy completeness. Finally, we use the Cauchy completeness of L-quasi-uniform convergence spaces to define the Cauchy completeness of L-quasi-uniform spaces, and show that Cauchy completeness is equivalent to Lawvere completeness in L-quasi-uniform spaces. | ||
کلیدواژهها | ||
L-quasi-uniform convergence space؛ L-quasi-uniform space؛ enriched category؛ Cauchy completeness؛ Lawvere completeness | ||
مراجع | ||
[1] R. Bˇelohl´avek, Fuzzy relation systems, foundation and principles, Klumer Academic/Plenum Publishers, New York - Boston - Dordrecht - London - Moscow, 2002. [2] Y. Chai, A note on the probabilistic quasi-metric spaces, Journal of Sichuan University (Natural Science Edition), 46 (2009), 543-547. [3] M. M. Clementino, D. Hofmann, On the completion monad via the Yoneda embedding in quasi-uniform spaces, Topology and its Applications, 158 (2001), 2423-2430. [4] M. M. Clementino, D. Hofmann, Topological features of lax algebras, Applied Categorical Structures, 11 (2003), 267-286. [5] M. M. Clementino, D. Hofmann, Lawvere completeness in topology, Applied Categorical Structures, 17 (2009), 175-210. [6] M. M. Clementino, D. Hofmann, W. Tholen, One setting for all: Metric, topology, uniformity, approach structure, Applied Categorical Structures, 12 (2004), 127-154. [7] C. H. Cook, H. R. Fischer, Uniform convergence structures, Mathematische Annalen, 173 (1967), 290-306.
[8] A. Craig, G. J¨ager, A common framework for latticed-valued uniform spaces and probabilistic uniform limit spaces, Fuzzy Sets and Systems, 160 (2009), 1177-1203. [9] P. Eklund, W. G¨ahler, Fuzzy filters, functors and convergence, Applications of Category Theory to Fuzzy Sets, (S. E. Rodabaugh, E. P. Klement, U. H¨ohle, Eds.), Kluwer, Dordrecht, 1992. [10] J. Fang, Lattice-valued semiuniform convergence spaces, Fuzzy Sets and Systems, 195 (2012), 33-57.
[11] J. Fang, Stratified L-ordered quasiuniform limit spaces, Fuzzy Sets and Systems, 227 (2013), 51-73.
[12] J. Fang, Lattice-valued preuniform convergence spaces, Fuzzy Sets and Systems, 251 (2014), 52-70.
[13] J. Guti´errez Garc´ıa, A unified approach to the concept of fuzzy L-uniform space, Thesis, Universidad del Pais Vasco, Bilbo, Spain, 2000. [14] J. Guti´errez Garc´ıa, M. A. De Prada Vicente, S. Romaguera, Completeness of Hutton [0, 1]-quasi-uniform spaces, Fuzzy Sets and Systems, 158(16) (2007), 1791-1802. [15] D. Hofmann, C. D. Reis, Probabilistic metric spaces as enriched categories, Fuzzy Sets and Systems, 210 (2013), 1-21. [16] D. Hofmann, W. Tholen, Lawvere completion and separation via closure, Applied Categorical Structures, 18 (2010), 259-287. [17] U. H¨ohle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Mathematica, 38 (1982), 289-323.
[18] U. H¨ohle, A. P. Sostak, ˇ Axiomatic foundations of fixed-basis fuzzy topology, Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, (U. H¨ohle, S. E. Rodabaugh, Eds.), Kluwer, Dordrecht, 1999. [19] G. J¨ager, A category of L-fuzzy convergence spaces, Quaestiones Mathematicae, 24 (2001), 501-517.
[20] G. J¨ager, M. H. Burton, Stratified L-uniform convergence spaces, Quaestiones Mathematicae, 28 (2005), 11-36.
[21] G. J¨ager, Y. Yue, ⊤-uniform convergence spaces, Iranian Journal of Fuzzy Systems, 19(2) (2022), 133-149.
[22] F. M. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matematico e Fisico di Milano, 43 (1973), 135-166. [23] R. S. Lee, The category of uniform convergence spaces is Cartesian-closed, Bulletin of the Australian Mathematical Society, 15 (1976), 461-465. [24] R. Lowen, Completeness, compactness and precompactness in fuzzy uniform spaces: Part I, Journal of Mathematical Analysis and Applications, 90(2) (1982), 563-581. [25] G. Preuss, Prefilter spaces and a precompletion of preuniform convergence spaces related to some well-known completions, Topology and Its Applications, 156(12) (2009), 2005-2012. [26] L. Reid, G. Richardson, Lattice-valued spaces: ⊤-completions, Fuzzy Sets and Systems, 369 (2019), 1-19.
[27] Y. Wang, Y. Yue, The applications of enriched category in lattice-valued quasi-uniformities, Fuzzy Systems and Mathematics, 35(03) (2021), 1-7. [28] Y. Wang, Y. Yue, Cauchy completion of fuzzy quasi-uniform spaces, Filomat, 35(12) (2021), 3983-4004.
[29] O. Wyler, Filter space monads, regularity, completions, TOPO 1972 - General Topology and its Applications, 591-637, Lecture notes in Mathematics, Vol. 378, Springer-Verlag, Berlin - Heidelberg - New York, 1974. [30] Y. Yue, J. Fang, Completeness in probabilistic quasi-uniform spaces, Fuzzy Sets and Systems, 370 (2019), 34-62.
[31] D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems, 158 (2007), 349-366 | ||
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