Connectedness in Jäger - Šostak's i-fuzzy topological spaces
DOI:
https://doi.org/10.4067/S0716-09172009000300002Keywords:
Jäger-Šostak's I-fuzzy topology, Subspace, The degree of connectedness, absolute property.Abstract
G.Jäger [Compactness and connectedness as absolute properties in fuzzy topological spaces, Fuzzy sets and Systems 94(1998) 405-401] introduced a kind of (general) fuzzy topological space. In this paper, we propose a new kind of topological space in Šostak's sense, called Jäger-Šostak's I-fuzzy topological space, which reduced to Jäger's (general) fuzzy topological to two-valued logic. After that for each fuzzy subset of Jäger-Šostak's I-fuzzy topological space, we define a degree of connectedness, which overcome the deficit of study for the whole space a degree of being connected in public papers, and establish two characteristic theorems of the degree of being connectedness. Doing so we find that the degree of connectedness is an absolute property in Jäger- Šostak's I-fuzzy topology.References
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[2] Fang J. M., Yue Y. L, Base and Subbase in I-fuzzy topological space, Journal of Mathematical Research and Exposition, 26(1), pp. 89—95, (2006).
[3] Fang J. M., Yue Y. L. Generalized connectivity, Proyecciones Journal of Mathematics 25(2), pp. 191—203, (2006).
[4] Fang J. M., Yue Y L. K. Fan’s theorem in fuzzifying topology, Information Sciences 162, pp. 139—146, (2004).
[5] Höhle U, Sostak A P. Axiomatic foundations of fixed basis fuzzy topology, Chapter 3 in: U. H¨ohle, S. E. Rodaubaugh (Eds.), Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory, Kluwer Academic Publishers, Boston/Dordrecht/London, pp. 123—272, (1999).
[6] Jäger G. Compactness and connectedness as absolute properties in fuzzy topological spaces, Fuzzy sets and Systems 94, pp. 405—401, (1998).
[7] Liu Y. M., Luo M. K. Induced spaces and fuzzy Stone-cech compacti- fications, Scientia Sinica (A) 30, pp. 1034—1044, (1987).
[8] Lowen R., Srivastava A. K., On Press’Connectedness concept in Fts, Fuzzy Set and Systems 47, pp. 99—104, (1992).
[9] Pu B. M., Liu Y. M. Fuzzy topology I-Neighborhood structure of a fuzzy point and Moon-Smith convergence, J. Math. Anal. Appl. 76, pp. 571—599, (1980).
[10] Werner P. Subspaces of smooth fuzzy topologies and initial smooth fuzzy structure, Fuzzy Sets and Systems 104, pp. 423—433, (1999).
[11] Ying M. S., A new approach to fuzzy topology (II), Fuzzy sets and systems 47, pp. 221—232, (1992).
How to Cite
[1]
F. Jinming and G. Yuanmei, “Connectedness in Jäger - Šostak’s i-fuzzy topological spaces”, Proyecciones (Antofagasta, On line), vol. 28, no. 3, pp. 209-226, 1.
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