اخبار و اعلانات
آمار
| تعداد نشریات | 27 |
| تعداد شماره‌ها | 558 |
| تعداد مقالات | 5,772 |
| تعداد مشاهده مقاله | 8,030,578 |
| تعداد دریافت فایل اصل مقاله | 5,397,699 |
QUANTALE-VALUED GAUGE SPACES | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 7، دوره 15، شماره 1، اردیبهشت 2018، صفحه 103-122 اصل مقاله (406.33 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.3581 | ||
| نویسندگان | ||
Gunther Jager  1؛ Wei Yao2
| ||
| 1University of Applied Sciences Stralsund, D-18435 Stralsund, Germany | ||
| 2Hebei University of Science and Technology, 050054 Shijiazhuang, P.R.China | ||
| چکیده | ||
| We introduce a quantale-valued generalization of approach spaces in terms of quantale-valued gauges. The resulting category is shown to be topological and to possess an initially dense object. Moreover we show that the category of quantale-valued approach spaces defined recently in terms of quantale-valued closures is a coreflective subcategory of our category and, for certain choices of the quantale, is even isomorphic to our category. Finally, the category of quantale-valued metric spaces is shown to be coreflectively embedded in our category. | ||
| کلیدواژه‌ها | ||
| $L$-gauge space؛ $L$-approach space؛ $L$-metric space؛ Continuity space | ||
| مراجع | ||
|
[1] S. Abramsky and A. Jung, Domain Theory, in: S. Abramsky, D.M. Gabby, T.S.E. Maibaum (Eds.), Handbook of Logic and Computer Science, Vol. 3, Claredon Press, Oxford, 1994. [2] J. Adamek., H. Herrlich and G. E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989. [3] R. C. Flagg, Quantales and continuity spaces, Algebra Univers., 37 (1997), 257 { 276. [4] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove and D. S. Scott, Continuous Lattices and Domains, Cambridge University Press, Cambridge, 2003. [5] J. Gutierrez Garca, On stratfii ed L-valued fi lters induced by >-fi lters, Fuzzy Sets and Systems 157 (2006), 813 { 819. [6] D. Hofmann, G. J. Seal and W. Tholen, Monoidal Topology - A Categorical Approach to Order, Metric and Topology, Cambridge University Press, Cambridge, 2014. [7] U. Hohle, Commutative, residuated l-monoids, in: Non-classical logics and their applications to fuzzy subsets (U. Hohle, E.P. Klement, eds.), Kluwer, Dordrecht (1995), 53 { 106. [8] G. Jager, A convergence theory for probabilistic metric spaces, Quaestiones Math., 38 (2015), 587{599. [9] G. Jager, Probabilistic approach spaces, Math. Bohemica, 142(3) (2017), 277-298. [10] H. Lai and W. Tholen, Quantale-valued topological spaces via closure and convergence, Topology Appl., 230 (2017), 599-620. [11] R. Lowen, Approach spaces: A common supercategory of TOP and MET, Math. Nachr., 141 (1989), 183 { 226. [12] R. Lowen, Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad, Clarendon Press, Oxford, 1997. [13] R. Lowen, Index Analysis, Springer-Verlag, London, 2015. [14] G. Preuss, Foundations of Topology. An Approach to Convenient Topology, Kluwer Academic Publishers, Dordrecht, 2002. [15] S. Saminger-Platz and C. Sempi, A primer on triangle functions I, Aequationes Math., 76 (2008), 201 { 240. [16] S. Saminger-Platz and C. Sempi, A primer on triangle functions II, Aequationes Math., 80 (2010), 239 { 261. [17] B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983. [18] W. Yao and B. Zhao, Kernel systems on L-ordered sets, Fuzzy Sets and Systems 182 (2011), 101 { 109. [19] W. Yao, A duality between -categories and algebraic -categories, Electronic Notes in Theoretical Computer Science, 301 (2014), 153 { 168. | ||
|
آمار تعداد مشاهده مقاله: 1,143 تعداد دریافت فایل اصل مقاله: 374 |
||
