Convergence in topological molecular lattices. (English) Zbl 0904.06006
Summary: The theory of topological molecular lattices introduced by Wang has general topology and fuzzy topology as special cases. In this paper, the author establishes the theory of ideal convergence in topological molecular lattices, and gives characterizations of some topological notions, e.g. closed elements, Hausdorffness, continuous GOH in topological molecular lattices, etc., in terms of ideals. The author establishes the relation between ideal convergence and molecular net convergence introduced by Wang.
Keywords:
remote-neighbourhoods; topological molecular lattices; fuzzy topology; ideal convergence; molecular net convergenceReferences:
| [1] | Chang, C. L., Fuzzy topological spaces, J. Math. Anal. Appl., 41, 478-485 (1973) · Zbl 0332.94001 |
| [2] | Chen, Y., Paracompactness on L-fuzzy topological spaces, Fuzzy Sets and Systems, 53, 335-342 (1993) · Zbl 0785.54006 |
| [3] | Hamburg, P.; Florescu, L., Topological structure in fuzzy lattices, J. Math. Anal. Appl., 101, 475-490 (1984) · Zbl 0599.54006 |
| [4] | Höhle, U., \(D\)-fuzzy topology on algebraic structures, J. Math. Anal. Appl., 108, 113-150 (1985) · Zbl 0602.54006 |
| [5] | Hutton, B., Uniformities in fuzzy topological spaces, J. Math. Anal. Appl., 58, 559-571 (1977) · Zbl 0358.54008 |
| [6] | Katsaras, A. K., Covergence in fuzzy topological spaces, Fuzzy Math., 3, 35-44 (1984) · Zbl 0569.54008 |
| [7] | Lowen, R., Convergence in fuzzy topology, Topology Appl., 10, 2, 147-160 (1979) · Zbl 0409.54008 |
| [8] | Lowen, R., The relation between filter and net convergence in fuzzy topological spaces, Fuzzy Math., 4, 41-52 (1983) · Zbl 0569.54007 |
| [9] | Pu, B.-M.; Liu, Y.-M., Fuzzy topology 1, neighbourhood structure of fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76, 571-599 (1980) · Zbl 0447.54006 |
| [10] | Wang, G.-J., A new fuzzy compactness defined by fuzzy nets, J. Math. Anal. Appl., 94, 1-23 (1983) · Zbl 0512.54006 |
| [11] | Wang, G.-J., Pointwise topology on completely distributive lattices, Fuzzy Sets and Systems, 30, 53-62 (1989) · Zbl 0667.54001 |
| [12] | Wang, G.-J., Theory of topological molecular lattices, Fuzzy Sets and Systems, 47, 351-376 (1992) · Zbl 0783.54032 |
| [13] | Warner, M. W., Fuzzy topology with respect to continuous lattices, Fuzzy Sets and Systems, 35, 85-91 (1990) · Zbl 0707.54004 |
| [14] | Warner, M. W., Frame — fuzzy points and membership, Fuzzy Sets and Systems, 42, 335-344 (1991) · Zbl 0741.54005 |
| [15] | Yang, Z.-Q., Ideals in topological molecular lattices, Acta Math. Sinica, 2, 276-279 (1986), (in Chinese) · Zbl 0609.06005 |
| [16] | Zadeh, L. A., Fuzzy sets, Inform. and Control, 8, 338-353 (1965) · Zbl 0139.24606 |
| [17] | Zhao, D.-S., The \(N\)-compactness in \(L\)-fuzzy topological spaces, J. Math. Anal. Appl., 128, 64-79 (1987) · Zbl 0639.54006 |
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.
