Lattice-valued convergence associated with CNS spaces. (English) Zbl 1423.54010
Summary: In this paper, in the context of meet continuous quantale, we present a notion of conical topological lattice-valued convergence space, which provides the theory of lattice-valued convergence associated with such conical neighborhood spaces.
MSC:
| 54A20 | Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) |
| 54A40 | Fuzzy topology |
| 06F07 | Quantales |
Keywords:
lattice-valued filters; lattice-valued convergence spaces; topological lattice-valued convergence spaces; conical neighborhood spacesReferences:
| [1] | Bělohlávek, R., Fuzzy Relational Systems: Foundations and Principles (2002), Kluwer Academic Publishers: Kluwer Academic Publishers New York · Zbl 1067.03059 |
| [2] | Fang, J. M., Stratified \(L\)-ordered convergence structures, Fuzzy Sets Syst., 161, 2130-2149 (2010) · Zbl 1197.54015 |
| [3] | Fang, J. M.; Yue, Y. L., ⊤-diagonal conditions and continuous extension theorem, Fuzzy Sets Syst., 321, 73-89 (2017) · Zbl 1379.54007 |
| [4] | Flores, P. V.; Mohapatra, R. N.; Richardson, G., Lattice-valued spaces: fuzzy convergence, Fuzzy Sets Syst., 157, 2706-2714 (2006) · Zbl 1123.54002 |
| [5] | Flores, P. V.; Richardson, G., Lattice-valued convergence: diagonal axioms, Fuzzy Sets Syst., 159, 2520-2528 (2008) · Zbl 1194.54007 |
| [6] | Gutiérrez García, J., On stratified \(L\)-valued filters induced by ⊤-filters, Fuzzy Sets Syst., 157, 813-819 (2006) · Zbl 1101.54006 |
| [7] | Gierz, G.; Hofmann, K. H.; Keimel, K.; Lawson, J. D.; Mislove, M. W.; Scott, D. S., Continuous Lattices and Domains (2003), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1088.06001 |
| [8] | Höhle, U.; Šostak, A., Axiomatic foundations of fixed-basis fuzzy topology, (Höhle, U.; Rodabaugh, S. E., Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, vol. 3 (1999), Kluwer Academic Publishers: Kluwer Academic Publishers Boston, Dordrecht, London), 123-273 · Zbl 0977.54006 |
| [9] | Jin, Q.; Li, L., One-axiom characterizations on lattice-valued closure (interior) operators, J. Intell. Fuzzy Syst., 31, 1679-1688 (2016) · Zbl 1367.54008 |
| [10] | Jin, Q.; Li, L., Modified top-convergence spaces and their relationships to lattice-valued convergence spaces, J. Intell. Fuzzy Syst. (2018), in press |
| [11] | Jin, Q.; Li, L., Stratified lattice-valued neighborhood tower group, Quaest. Math. (2018) · Zbl 1427.54016 |
| [12] | Jin, Q.; Li, L.; Meng, G., On the relationships between types of \(L\)-convergence spaces, Iran. J. Fuzzy Syst., 1, 93-103 (2016) · Zbl 1350.54007 |
| [13] | Jin, Q.; Li, L.; Lv, Y., Connectedness for lattice-valued subsets in lattice-valued convergence spaces, Quaest. Math. (2018) |
| [14] | Jäger, G., A category of \(L\)-fuzzy convergence spaces, Quaest. Math., 24, 501-517 (2001) · Zbl 0991.54004 |
| [15] | Jäger, G., Fischer’s diagonal condition for lattice-valued convergence spaces, Quaest. Math., 31, 11-25 (2008) · Zbl 1168.54005 |
| [16] | Jäger, G., Gähler’s neighbourhood condition for lattice-valued convergence spaces, Fuzzy Sets Syst., 204, 27-39 (2012) · Zbl 1271.54036 |
| [17] | Jäger, G., Stratified LMN-convergence tower spaces, Fuzzy Sets Syst., 282, 62-73 (2016) · Zbl 1392.54005 |
| [18] | Lai, H.; Zhang, D., Fuzzy topological spaces with conical neighborhood systems, Fuzzy Sets Syst., 330, 87-104 (2018) · Zbl 1380.54009 |
| [19] | Li, L.; Jin, Q., On adjunctions between Lim, \(SL\)-Top, and \(SL\)-Lim, Fuzzy Sets Syst., 182, 66-78 (2011) · Zbl 1244.54018 |
| [20] | Li, L.; Jin, Q., On stratified \(L\)-convergence spaces: pretopological axioms and diagonal axioms, Fuzzy Sets Syst., 204, 40-52 (2012) · Zbl 1254.54010 |
| [21] | Li, L.; Jin, Q., \(p\)-topologicalness and \(p\)-regularity for lattice-valued convergence spaces, Fuzzy Sets Syst., 238, 26-45 (2014) · Zbl 1315.54007 |
| [22] | Li, L.; Jin, Q.; Hu, K., On stratified \(L\)-convergence spaces: Fischer’s diagonal axiom, Fuzzy Sets Syst., 267, 31-40 (2015) · Zbl 1392.54010 |
| [23] | Li, L.; Jin, Q.; Hu, K., The axiomatic characterizations on \(L\)-fuzzy covering-based approximation operators, Int. J. Gen. Syst., 46, 332-353 (2017) |
| [24] | Li, L.; Jin, Q.; Meng, G. W., The lower and upper \(p\)-topological \((p\)-regular) modifications for lattice-valued convergence spaces, Fuzzy Sets Syst., 282, 47-61 (2016) · Zbl 1392.54011 |
| [25] | Lowen, R., Convergence in fuzzy topological spaces, Topol. Appl., 10, 147-160 (1979) · Zbl 0409.54008 |
| [26] | Orpen, D.; Jäger, G., Lattice-valued convergence spaces: extending the lattice context, Fuzzy Sets Syst., 190, 1-20 (2012) · Zbl 1241.54004 |
| [27] | Pang, B.; Zhao, Y., Several types of enriched \((L, M)\)-fuzzy convergence spaces, Fuzzy Sets Syst., 321, 55-72 (2017) · Zbl 1375.54004 |
| [28] | Pang, B., Degrees of separation properties in stratified \(L\)-generalized convergence spaces using residual implication, Filomat, 31, 20, 6293-6305 (2017) · Zbl 1499.54057 |
| [29] | Pang, B., Stratified \(L\)-ordered filter spaces, Quaest. Math., 40, 661-678 (2017) · Zbl 1422.54006 |
| [30] | Qiu, Y.; Fang, J. M., The category of all ⊤-convergence spaces and its cartesian-closedness, Iran. J. Fuzzy Syst., 14, 3, 121-138 (2017) · Zbl 1398.54007 |
| [31] | Reid, L.; Richardson, G., Connecting ⊤ and lattice-valued convergences, Iran. J. Fuzzy Syst. (2017) · Zbl 1400.54005 |
| [32] | Rosenthal, K. I., Quantales and Their Applications (1990), Longman Scientific & Technical · Zbl 0703.06007 |
| [33] | Yang, X.; Li, S., Completion of stratified \((L, M)\)-filter tower spaces, Fuzzy Sets Syst., 210, 22-38 (2013) · Zbl 1260.54027 |
| [34] | Yao, W., On many-valued stratified \(L\)-fuzzy convergence spaces, Fuzzy Sets Syst., 159, 2503-2519 (2008) · Zbl 1206.54012 |
| [35] | Yao, W., Moore-Smith convergence in \((L, M)\)-fuzzy topology, Fuzzy Sets Syst., 190, 47-62 (2012) · Zbl 1250.54009 |
| [36] | Zhang, D., An enriched category approach to many valued topology, Fuzzy Sets Syst., 158, 349-366 (2007) · Zbl 1112.54005 |
| [37] | Zhao, F.; Jin, Q.; Li, L., The axiomatic characterizations on \(L\)-generalized fuzzy neighborhood system-based approximation operators, Int. J. Gen. Syst., 47, 2, 155-173 (2018) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
