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Diagonal conditions and uniformly continuous extension in $\top$-uniform limit spaces | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 10، دوره 19، شماره 5، آذر و دی 2022، صفحه 131-145 اصل مقاله (227.48 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2022.7161 | ||
| نویسنده | ||
| G. Jager* | ||
| University of Applied Sciences Stralsund, Stralsund, Germany | ||
| چکیده | ||
| We study suitable diagonal conditions for $\top$-uniform limit spaces. A dual diagonal condition is shown to be a suitable axiom for uniform regularity. We characterize this regularity concept by closures of $L$-sets. We apply all these diagonal axioms and prove an extension theorem for uniformly continuous mappings defined on a dense subspace. | ||
| کلیدواژهها | ||
| Topology؛ top-filter؛ uniform limit space؛ lattice-valued uniform convergence space؛ probabilistic uniform space؛ diagonal axiom؛ uniform regularity؛ extension of mappings | ||
| مراجع | ||
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[1] J. Adámek., H. Herrlich, G. E. Strecker, Abstract and concrete categories, Wiley, New York, 1989.
[2] R. Bĕlohlávek, Fuzzy relation systems, foundation and principles, Klumer Academic/Plenum Publishers, New York, Boston, Dordrecht, London, Moscow, 2002.
[3] A. Craig, G. Jäger, A common framework for lattice-valued uniform spaces and probabilistic uniform limit spaces, Fuzzy Sets and Systems, 160 (2009), 1177-1203.
[4] J. Fang, Y. Yue, ⊤-diagonal conditions and continuous extension theorem, Fuzzy Sets and Systems, 321 (2017), 73-89.
[5] R. C. Flagg, Quantales and continuity spaces, Algebra Universalis, 37 (1997), 257-276.
[6] W. Gähler, Grundstrukturen der analysis I, Birkhäuser, Basel, 1977.
[7] G. Gierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, D. S. Scott, Continuous lattices and domains, Cambridge University Press, 2003.
[8] U. Höhle, Probabilistic topologies induced by L-fuzzy uniformities, Manuscripta Mathematica, 38 (1982), 289-323.
[9] U. Höhle, Commutative, residuated l-monoids, in: Non-classical logics and their applications to fuzzy subsets (U. Höhle, E.P. Klement, eds.), Kluwer, Dordrecht, (1995), 53-106.
[10] D. Hofmann, G. J. Seal, W. Tholen, Monoidal topology, Cambridge University Press, Cambridge, 2014.
[11] G. Jäger, Diagonal conditions for lattice-valued uniform convergence spaces, Fuzzy Sets and Systems, 210 (2013), 39-53.
[12] G. Jäger, M. Burton, Stratified L-uniform convergence spaces, Quaestiones Mathematicae, 28 (2005), 11-36.
[13] G. Jäger, Y. Yue, ⊤-uniform convergence spaces, Iranian Journal of Fuzzy Systems, 19(2) (2022), 133-149.
[14] H. J. Kowalsky, Limesräume und komplettierung, Mathematische Nachrichten, 12 (1954), 301-340.
[15] F. W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matematico e Fisico di Milano, 43 (1973), 135-166. Reprinted in: Reprints in Theory and Applications of Categories 1 (2002), 1-37.
[16] L. Li, p-Topologicalness - A relative topologicalness in T-convergence spaces, Mathematics, 7 (2019), 228. DOI:10.3390/math7030228.
[17] L. Reid, G. Richardson, Connecting ⊤ and lattice-valued convergences, Iranian Journal of Fuzzy Systems, 15(4) (2018), 151-169.
[18] L. Reid, G. Richardson, Lattice-valued spaces: ⊤-completions, Fuzzy Sets and Systems, 369 (2019), 1-19.
[19] B. Schweizer, A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
[20] Q. Yu, J. Fang, The category of ⊤-convergence spaces and its Cartesian-closedness, Iranian Journal of Fuzzy Systems, 14(3) (2017), 121-138.
[21] Y. Yue, J. Fang, Completeness in probabilistic quasi-uniform spaces, Fuzzy Sets and Systems, 370 (2019), 34-62.
[22] D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems, 158 (2007), 349-366. | ||
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