تعداد نشریات | 27 |
تعداد شمارهها | 557 |
تعداد مقالات | 5,770 |
تعداد مشاهده مقاله | 8,025,710 |
تعداد دریافت فایل اصل مقاله | 5,394,475 |
A COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 6، دوره 14، شماره 3، شهریور 2017، صفحه 67-81 اصل مقاله (430.13 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2017.3256 | ||
نویسنده | ||
Gunther Jager ![]() | ||
School of Mechanical Engineering, University of Applied Sciences Stralsund, 18435 Stralsund, Germany | ||
چکیده | ||
We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabilistic and approach uniform convergence spaces as examples. We show that the resulting category $sLMN$-$UCTS$ is topological, well-fibred and Cartesian closed. We furthermore define stratified $LMN$-uniform tower spaces and show that the category of these spaces is isomorphic to the subcategory of stratified $LMN$-principal uniform convergence tower spaces. Finally we study the underlying stratified $LMN$-convergence tower spaces. | ||
کلیدواژهها | ||
Stratified lattice-valued uniformity؛ Stratified lattice-valued uniform convergence space؛ Probabilistic uniform convergence space؛ Approach uniform convergence space؛ Stratified $LM$-filter | ||
مراجع | ||
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete categories, Wiley, New York 1989. [2] T. M. G. Ahsanullah and G. Jager, Probabilistic uniform convergence spaces redened, Acta Math. Hungar., 146 (2015), 376 { 390. [3] N. Bourbaki, General topology, Chapters 1 { 4, Springer Verlag, Berlin - Heidelberg - New York - London - Paris - Tokyo, 1990. [4] M. H. Burton, M. A. de Prada Vicente and J. Gutierrez Garca, Generalized uniform spaces, J. Fuzzy Math., 4 (1996), 363 { 380. [5] C. H. Cook and H. R. Fischer, Uniform convergence structures, Math. Ann. 173 (1967), 290 { 306. [6] A. Craig and G. Jager, A common framework for lattice-valued uniform spaces and proba- bilistic uniform limit spaces, Fuzzy Sets and Systems, 160(2009), 1177 { 1203. [7] J. Fang, Lattice-valued semiuniform convergence spaces, Fuzzy Sets and Systems, 195 (2012), 33 { 57. [8] R. C. Flagg, Quantales and continuity spaces, Algebra Univers., 37 (1997), 257 { 276. [9] L. C. Florescu, Probabilistic convergence structures, Aequationes Math., 38 (1989), 123 { 145. [10] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. Mislove and D. S. Scott, A com- pendium of continuous lattices, Springer-Verlag Berlin Heidelberg, 1980. [11] J. Gutierrez Garca, A unied approach to the concept of fuzzy L-uniform space, Thesis, Universidad del Pais Vasco, Bilbao, Spain, 2000. [12] J. Gutierrez Garca, M. A. de Prada Vicente and A. P. Sostak, A unied approach to the concept of fuzzy L-uniform space, In: S. E. Rodabaugh, E. P. Klement (Eds.), Topological and algebraic structures in fuzzy sets, Kluwer, Dordrecht, (2003), 81 { 114. [13] U. Hohle, Characterization of L-topologies by L-valued neighborhoods, In: U. Hohle, S.E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory, Kluwer, Boston/Dordrecht/London 1999, 389 { 432. [14] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, In: U. Hohle, S. E. Rodabauch (Eds.), Mathematics of Fuzzy Sets. Logic, Topology and Measure Theory, Kluwer, Boston/Dordrecht/London 1999, 123 { 272. [15] G. Jager, A category of L-fuzzy convergence spaces, Quaestiones Math., 24 (2001), 501 { 518. [16] G. Jager, Fischer's diagonal condition for lattice-valued convergence spaces, Quaestiones Math., 31 (2008), 11 { 25. [17] G. Jager, A note on stratied LM-lters, Iranian Journal of Fuzzy Systems, 10(4) (2013), 135 { 142. [18] G. Jager, Stratied LMN-convergence tower spaces, Fuzzy Sets and Systems, 282 (2016), 62 { 73. [19] G. Jager, Uniform connectedness and uniform local connectedness for lattice-valued uniform convergence spaces, Iranian Journal of Fuzzy Systems, 13(3) (2016), 95 { 111. [20] G. Jager and M. H. Burton, Stratied L-uniform convergence spaces, Quaestiones Math., 28 (2005), 11 { 36. [21] Y. J. Lee and B. Windels, Transitivity in uniform approach theory, Int. J. Math. and Math. Sci., 32 (2002), 707 { 720. [22] E. Lowen, R. Lowen and P. Wuyts, The categorical topology approach to fuzzy topology and fuzzy convergence, Fuzzy Sets and Systems, 40 (1991), 347 { 373. [23] R. Lowen and B. Windels, AUnif: A commmon supercategory of pMET and Unif, Int. J. Math. and Math. Sci., 21 (1998), 1 { 18. [24] H. Nusser, A generalization of probabilistic uniform spaces, Appl. Cat. Structures, 10 (2002), 81 { 98. [25] G. Preuss, Foundations of topology - An Approach to Convenient Topology, Kluwer, Dordrecht 2002. [26] B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983. [27] O. Wyler, Filter space monads, regularity, completions, In: TOPO 1972 | General Topology and its Applications, Lecture Notes in Mathematics, Vol.378, Springer, Berlin, Heidelberg, New York, (1974), 591 { 637. | ||
آمار تعداد مشاهده مقاله: 634 تعداد دریافت فایل اصل مقاله: 480 |