| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,852,494 |
| تعداد دریافت فایل اصل مقاله | 9,586,515 |
$L$-enriched topological systems---a common framework of $L$-topology and $L$-frames | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 9، دوره 11، شماره 5، دی 2014، صفحه 93-103 اصل مقاله (370.14 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2014.1725 | ||
| نویسنده | ||
| M. Liu* | ||
| School of Sciences, Chang'an University, Xi'an, China | ||
| چکیده | ||
| Employing the notions of the strong $L$-topology introduced by Zhang and the $L$-frame introduced by Yao and the concept of $L$-enriched topological system defined in the present paper, we construct adjunctions among the categories {\bf St$L$-Top} of strong $L$-topological spaces, {\bf S$L$-Loc} of strict $L$-locales and {\bf $L$-EnTopSys} of $L$-enriched topological systems. All of these concepts are essentially based on the theory of $L$-enriched categories, thus we obtain a unified enriched-categorical version of the classical adjunctions among the categories {\bf Top} of topological spaces, {\bf Loc} of locales and {\bf TopSys} of topological systems, as well as a unified enriched-categorical approach to treating these concepts. | ||
| کلیدواژهها | ||
| Enriched category؛ Adjunction؛ $L$-ordered set؛ Strong $L$-topology؛ $L$-enriched topological system؛ $L$-frame | ||
| مراجع | ||
|
\bibitem{Adamek:ACC} J. Ad\'{a}mek, H. Herrlich and G. E. Strecker, {\it Abstract and Concrete Categories}, Wiley, New York, 1990. \bibitem{Belohlavek:CLAO} R. B\v{e}lohl\'{a}vek, {\it Concept lattices and order in fuzzy logic}, Annals of Pure and Applied Logic, {\bf 128(1-3)} (2004), 277-298. \bibitem{Belohlavek:FRA} R. B\v{e}lohl\'{a}vek, {\it Fuzzy relational systems: foundations and principles}, Kluwer Academic/Plenum Publishers, New York, 2002. \bibitem{Chang:FTS} C. L. Chang, {\it Fuzzy topological spaces}, J. Math. Anal. Appl., {\bf 24(1)} (1968), 182-190. \bibitem{Denniston:ETS} J. T. Denniston, A. Melton and S. E. Rodabaugh, {\it Enriched topological systems and variable-basis enriched functors}, In: U. H\"{o}hle, L. N. Stout, E. P. Klement, Abstracts of the 33th Linz Seminar on Fuzzy Set Theory, Universit\"{a}tsdirektion Johannes Kepler Universit\"{a}t (Linz, Austria), 14-18 February (2012), 16-20. \bibitem{Denniston:IAAT} J. T. Denniston, A. Melton and S. E. Rodabaugh, {\it Interweaving algebra and topology: Lattice-valued topological systems}, Fuzzy Sets and Systems, {\bf 192} (2012), 58-103. \bibitem{Denniston:LTS} J. T. Denniston, A. Melton and S. E. Rodabaugh, {\it Lattice-valued topological systems}, In: U. Bodenhofer, B. De Baets, E. P. Klement, Abstracts of the 30th Linz Seminar, Universit\"{a}tsdirektion Johannes Kepler Universit\"{a}t (Linz, Austria), 3-7 February (2009), 24-31. \bibitem{Fan:ANAT}L. Fan, {\it A new approach to quantitative domain theory}, Electronic Notes in Theoretical Computer Science, {\bf 45} (2001), 77-87. \bibitem{Goguen:LFS} J. A. Goguen, {\it $L$-fuzzy sets}, Journal of Mathematical Analysis and Applications, {\bf 18(1)} (1967), 145-174. \bibitem{Goguen:TFTT} J. A. Goguen, {\it The fuzzy tychonoff theorem}, J. Math. Anal. Appl., {\bf 43(3)} (1973), 734-742. \bibitem{Hofmann:AIQC} D. Hofmann and P. L. Waszkiewicz, {\it Approximation in quantale-enriched categories}, Topology and its Applications, {\bf 158(8)} (2011), 963-977. \bibitem{Johnstone:SS} P. T. Johnstone, {\it Stone spaces}, Cambridge University Press, Cambridge, 1982. \bibitem{Kelly:BCOE} G. M. Kelly, {\it Basic concepts of enriched category theory}, London Mathematical Society Lecture Notes Series 64, Cambridge University Press, 1982. \bibitem{Lai:CADC} H. Lai and D. Zhang, {\it Complete and directed complete $\Omega$-categories}, Theoret. Comput. Sci., {\bf 388(1-3)} (2007), 1-25. \bibitem{Lai:MCD} H. Lai and D. Zhang, {\it Many-valued complete distributivity}, arXiv:math/0603590v2 [math.CT], 12 May 2006. \bibitem{Lawvere:MSGL} F. W. Lawvere, {\it Metric spaces, generalized logic, and closed categories}, Rend. Sem. Mat. Fis. Milano, {\bf 43(1)} (1973), 135-166. \bibitem{Liu:OSRP} M. Liu, {\it On some related problems in $\Omega$-categories and fuzzy domains}, Ph.D. Thesis, Shannxi normal university, Xi'an, China, 2013. \bibitem{Lowen:FTSA} R. Lowen, {\it Fuzzy topological spaces and fuzzy compactness}, J. Math. Anal. Appl., {\bf 56(3)} (1976), 623-633. \bibitem{Rodabaugh:POFF} S. E. Rodabaugh, {\it Powerset operator foundations for poslat fuzzy set theories and topologies}, in: U. H\"{o}hle, S. E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The Handbooks of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, (1999), 91-116. \bibitem{Rosenthal:QATA} K. I. Rosenthal, {\it Quantales and Their Applications}, Pitman Research Notes in Mathematics Series, Longman, {\bf 234} (1990). \bibitem{Stubbe:CSCD} I. Stubbe, {\it Categorical structures enriched in a quantaloid: Categories, distributors and functors}, Theory Appl. Categ., {\bf 14(1)} (2005), 1-45. \bibitem{Stubbe:CSTA} I. Stubbe, {\it Categorical structures enriched in a quantaloid: Tensored and cotensored categories}, Theory Appl. Categ., {\bf 16(14)} (2006), 283-306. \bibitem{Vickers:TVL} S. J. Vickers, {\it Topology via logic}, Cambridge University Press, Cambridge, 1989. \bibitem{Wagner:SRDE} K. R. Wagner, {\it Solving recursive domain equations with enriched categories}, Ph.D. Thesis, Carnegie Mellon University, Tech. Report CMU-CS-94-159, July, 1994. \bibitem{Yao:AATF} W. Yao, {\it An approach to fuzzy frames via fuzzy posets}, Fuzzy Sets and Systems, {\bf 166(1)} (2011), 75-89. \bibitem{Yao:QDVF} W. Yao, {\it Quantitative domains via fuzzy sets: Part I: continuity of fuzzy directed-complete poset}, Fuzzy Sets and Systems, {\bf 161(7)} (2010), 983-987. \bibitem{Zhang:AECA} D. Zhang, {\it An enriched category approach to many valued topology}, Fuzzy Sets and Systems, {\bf 158(4)} (2007), 349-366. \bibitem{Zhang:FCL} Q. Y. Zhang, W. X. Xie and L. Fan, {\it Fuzzy complete lattices}, Fuzzy Sets and Systems, {\bf 160(16)} (2009), 2275-2291. | ||
|
آمار تعداد مشاهده مقاله: 2,349 تعداد دریافت فایل اصل مقاله: 1,269 |
||