اخبار و اعلانات
آمار
| تعداد نشریات | 29 |
| تعداد شماره‌ها | 630 |
| تعداد مقالات | 6,368 |
| تعداد مشاهده مقاله | 9,731,571 |
| تعداد دریافت فایل اصل مقاله | 6,362,970 |
Subcategories of the category of stratified $(L,M)$-semiuniform convergence tower spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 14 تیر 1402 اصل مقاله (224.31 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2023.43934.7736 | ||
| نویسندگان | ||
| Lin Zhang1؛ Bin Pang* 2؛ Wenbo Li3 | ||
| 1Beijing Institute of Technology | ||
| 2School of Mathematics, Beijing Institute of Technology | ||
| 3Mudanjiang Normal University | ||
| چکیده | ||
| In this paper, we propose the concepts of stratified (L,M)-semiuniform convergence spaces and stratified (L,M)-semiuniform limit tower spaces. It is shown that (1) the category S(L,M)-SUC of stratified (L,M)-semiuniform convergence spaces can be embedded in the category S(L,M)- SUCT of stratified (L,M)-semiuniform convergence tower spaces as a bireflective subcategory; (2) the full subcategory of S(L,M)-SUCT, consisting of stratified (L,M)-semiuniform limit tower spaces is strongly Cartesian closed; (3) the category S(L,M)-FT of stratified (L,M)-filter tower spaces can be embedded in the category S(L,M)-SUCT as a simultaneously bireflective and bicoreflective subcategory. | ||
| کلیدواژه‌ها | ||
| M)-semiuniform convergence space؛ (L؛ M)-filter tower space؛ Strongly Cartesian closed؛ bireflective؛ bicoreflective | ||
| مراجع | ||
|
[1] J. Adamek, H. Herrlich, G. E. Strecker, Abstract and concrete categories, Wiley, New York, 1990. [2] C. H. Cook, H. R. Fischer, Uniform convergence structures, Mathematische Annalen, 173 (1967), 290-306. [3] J. M. Fang, Strati ed L-ordered convergence structures, Fuzzy Sets and Systems, 161 (2010), 2130-2149.
[4] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies, Fuzzy Sets and Systems, 161 (2010), 2923-2944.
[5] J. M. Fang, Lattice-valued semiuniform convergence spaces, Fuzzy Sets and Systems, 195 (2012), 33-57.
[6] J. M. Fang, Strati ed L-ordered quasiuniform limit spacesv, Fuzzy Sets and Systems, 227 (2013), 51-73.
[7] J. M. Fang, Lattice-valued preuniform convergence spaces, Fuzzy Sets and Systems, 251 (2014), 52-70.
[8] J. M. Fang, Z. Fang, Monoidal closedness of the category of strati ed L-semiuniform convergence spaces, Fuzzy Sets and Systems, 425 (2021), 83-99.
[9] J. M. Fang, Y. L. Yue, A one to one correspondence between connected varieties and disconnected varieties of ⊤-semiuniform convergence spaces, Fuzzy Sets and Systems, (2022). DOI: 10.1016/j.fss.2022.10.010.
[10] J. Gutierrez Garca, A uni ed approach to the concept of fuzzy L-uniform space, Thesis, Universidad del Pais Vasco, Bilbao, Spain, 2000.
[11] U. Hohle, Probabilistic metrization of fuzzy uniformities, Fuzzy Sets and Systems, 8 (1982), 63-69.
[12] U. Hohle, Many valued topology and its applications, Kluwer Academic Publishers, Boston, Dordrecht, London, 2001.
[13] U. Hohle, A. P. Sostak, Axiomatic foudations of xed-basis fuzzy topology, in: U. Hohle, S.E. Rodabaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, Handbook Series, Vol. 3, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, 123-173.
[14] B. Hutton, Uniformities on fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 58(3)(1977), 559-571.
[15] G. Jager, A category of L-fuzzy convergence spaces, Quaestiones Mathematicae, 24 (2001), 501-517.
[16] G. Jager, Subcategories of lattice-valued convergence spaces, Fuzzy Sets and Systems, 156 (2005), 1-24.
[17] G. Jager, Level spaces for lattice-valued uniform convergence spaces, Quaestiones Mathematicae, 31 (2008), 255-277.
[18] G. Jager, Lattice-valued Cauchy spaces and completion, Quaestiones Mathematicae, 33 (2010), 53-74.
[19] G. Jager, A common framework for lattice-valued, probabilistic and approach uniform (convergence) spaces, Iranian Journal of Fuzzy Systems, 14(3) (2017), 67-81.
[20] G. Jager, Diagonal conditions and uniformly continuous extension in ⊤-uniform limit spaces, Iranian Journal of Fuzzy Systems, 19(5) (2022), 131-145.
[21] G. Jager, M. H. Burton, Strati ed L-uniform convergence spaces, Quaestiones Mathematicae, 28 (2005), 11-36.
[22] G. Jager, Y. Yue, ⊤-uniform convergence spaces, Iranian Journal of Fuzzy Systems, 19(2) (2022), 133-149.
[23] R. S. Lee, The category of uniform convergence spaces is Cartesian-closed, Bulletin of the Australian Mathematical Society, 15 (1976), 461-465.
[24] J. Li, Strati ed (L,M)-semiuniform convergence tower spaces, Iranian Journal of Fuzzy Systems, 16(2) (2019), 87-96.
[25] L. Q. Li, Q. Jin, On adjunctions between Lim, SL-Top, and SL-Lim, Fuzzy Sets and Systems, 182 (2011), 66-78.
[26] M. Nauwelaerts, (Quasi-)semi-approach uniform convergence spaces, Scientiae Mathematicae Japonicae, 4 (2001), 669-697.
[27] H. Nusser, A generalization of probabilistic uniform spaces, Applied Categorical Structures, 10(1) (2002), 81-98.
[28] B. Pang, The category of strati ed L- lter spaces, Fuzzy Sets and Systems, 247 (2014), 108-126.
[29] G. Preuss, Foundations of topology{An approach to convenient topology, Kluwer Academic Publisher, Dordrecht, Boston, London, 2002.
[30] L. Reid, G. Richardson, Lattice-valued spaces: ⊤-completions, Fuzzy Sets and Systems, 369 (2019), 1-19.
[31] S. E. Rodabaugh, Categorical foundations of variable-basis fuzzy topology, Mathematics of Fuzzy Sets, 273-388. DOI: 10.1007/978-1-4615-5079-2 6.
[32] A. Weil, Sur les espaces a structures uniformes et sur la topologie generale, Actualites Scienti ques et Industrielles, Vol. 551, Hermann, Paris, 1937.
[33] O. Wyler, Filter space monads, regularity, completions, TOPO 1972{General Topology and its Applications, Lecture Notes in Mathematics, Vol. 378., Springer, Berlin, Heidelberg, New York, (1974), 591-637.
[34] X. F. Yang, S. G. Li, Completion of strati ed (L,M)- lter tower spaces, Fuzzy Sets and Systems, 210 (2013), 22-38.
[35] L. Zhang, B. Pang, Monoidal closedness of the category of ⊤-semiuniform convergence spaces, Hacettepe Journal of Mathematics and Statistics, 51(5) (2022), 1348-1370.
36] L. Zhang, B. Pang, The category of residuated lattice valued lter spaces, Quaestiones Mathematicae, 45(11) (2022), 1795-1821.
[37] L. Zhang, B. Pang, A new approach to lattice-valued convergence groups via ⊤- lters, Fuzzy Sets and Systems, 455 (2023), 198-221.
[38] L. Zhang, B. Pang, Convergence structures in (L,M)-fuzzy convex spaces, Filomat, 37(9) (2023), 2859-2877. | ||
|
آمار تعداد مشاهده مقاله: 32 تعداد دریافت فایل اصل مقاله: 49 |
||