?-separation axioms based on Lukasiewicz logic

In the present paper, we introduce topological notions defined by meansof ?-open sets when these are planted into the framework of Ying'sfuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T?-, T?1-, T?2(?- Hausdorff)-, T?3(?-regular)- and T?(?normal)-separation axioms. Furthermore, the R0- and R?- separation axioms are studied and their relations with the T?1- and T?2-separation axioms are introduced. Moreover, we clarify the relationsof these axioms with each other as well as the relations with otherfuzzifying separation axioms.

PDF

___

I. W. Alderton, ?-compactness of fuzzy topological spaces: A categorical approach, Quas- tiones Mathematicae, 20 (1997), 269-282.
M. Caldas, D. N. Georgiou and S. Jafari, Characterizations of Low separation axioms via ?-open sets and ?-closure operator, Bol. Soc. Paran. Mat., 21 (1-2)(2003), 1-14.
M. Caldas, S. Jafari R. M. Latif and T. Noiri, Characterizations of functions with strongly ?-closed graphs, Scientific Studies and Research Series Mathematics and Informatics 19 (1)(2009), 49-58.
C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
J. A. Goguen, The fuzzy Tychonoff theorem, J. Math.Anal. Appl., 43 (1973), 182-190.
U. H¨ohle, Uppersemicontinuous fuzzy sets and applications, J. Math. Anal. Appl., 78 (1980), 659-673.
U. H¨ohle, Many Valued Topology and its Applications, Kluwer Academic Publishers, Dor- drecht, 2001.
U. H¨ohle, S. E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in: Handbook of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, 1999.
U. H¨ohle, S. E. Rodabaugh, A. ^Sostak, (Eds.), Special Issue on Fuzzy Topology, Fuzzy Sets and Systems, 73 (1995), 1-183.
U. H¨ohle, A. ^Sostak, Axiomatic foundations of fixed-basis fuzzy topology, in: U. H¨ohle, S. E. Rodabaugh, (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in: Handbook of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, 1999, 123-272.
J. L. Kelley, General Topology, Van Nostrand, New York, 1955.
F. H. Khedr, F. M. Zeyada and O. R. Sayed, ?-continuity and c?-continuity in fuzzifying topology, Fuzzy Sets and Systems, 116 (2000), 325-337.
F.H. Khedr, F.M. Zeyada, O.R. Sayed, On separation axioms in fuzzifying topology Fuzzy Sets and Systems 119 (2001), 439-458.
T. Kubiak, On Fuzzy Topologies, Ph.D. Thesis, Adam Mickiewicz University, Poznan, Poland, 1985
Y. M. Liu, M. K. Luo, Fuzzy Topology, World Scientific, Singapore, 1998.
S. N. Maheshwari and S. S. Thakur, On ?-irresolute mappings, Tamkang J. Math., 11 (1980) 209-214.
M. Maki, R. Devi and K. Balachandran,Generalized ?-closed sets in topology, Bull. Fukuoka Univ. Ed. Part III, 42 (1993) 13-21.
A. N. Mahshour M. H. Ghanim and M. A. Fathalla, ?-separation axioms and ?-compactness in fuzzy topological spaces, Rocky Mountain Journal of Mathematics, 16 (3)(1986) 591-600.
T. Noiri, On ?-continuous functions, ~Casopis P?est. Mat., 109 (1984) 118-126.
D. Qiu, Characterizations of fuzzy finite automata, Fuzzy Sets and Systems, 141 (2004) 391-414.
D. Qiu, Fuzzifying topological linear spaces, Fuzzy Sets and Systems, 147 (2004) 249-272.
I. L. Reilly and M. K. Vamanamurthy, On ?-sets in topological spaces, Tamkang J. Math., 16 (1985) 7-11.
S. E. Rodabaugh, Categorical foundations of variable-basis fuzzy topology, in: U. H¨ohle, S. E. Rodabaugh, (Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in: Handbook of Fuzzy Sets Series, vol. 3, Kluwer Academic Publishers, Dordrecht, 1999, 273-388.
S. E. Rodabaugh, The Hausdorff separation axioms for fuzzy topological spaces, Topology Appl., 11 (1980) 319-334.
J. B. Rosser, A. R. Turquette, Many-Valued Logics, North-Holland, Amsterdam, 1952.
J. Shen, Separation axiom in fuzzifying topology, Fuzzy Sets and Systems 57 (1993), 111- 123.
G. J. Wang, Theory of L-Fuzzy Topological Spaces, Shanxi Normal University Press, Xi an, 1988 (in Chinese).
M. S. Ying, A new approach for fuzzy topology (I), Fuzzy Sets and Systems, 39 (1991), 303-321.
M. S. Ying, A new approach for fuzzy topology (II), Fuzzy Sets and Systems, 47 (1992), 221-23.
M. S. Ying, A new approach for fuzzy topology (III), Fuzzy Sets and Systems, 55 (1993), 193-207.
M. S. Ying, Fuzzifying topology based on complete residuated lattice-valued logic (I), Fuzzy Sets and Systems, 56 (1993), 337-373.
M. S. Ying, Fuzzy Topology Based on Residuated Lattice-Valued Logic, Acta Mathematica Sinica, 17 (2001), 89-102.

Hacettepe Journal of Mathematics and Statistics-Cover

Yayın Aralığı: Yılda 6 Sayı
Başlangıç: 2002
Yayıncı: Hacettepe Üniversitesi Fen Fakultesi

Arşiv