## Some other types of fuzzy connectedness.(English)Zbl 0759.54003

Various concepts of fuzzy connectedness are investigated. $$\alpha$$-level connectedness concepts $$\alpha$$-$$C3$$ and $$\alpha$$-$$C4$$ are introduced and studied. Some of the theorems are as follows. The following are equivalent: (1) $$(X,t)$$ is $$\alpha$$-$$C4$$; (2) $$(X,i_{1-\alpha}(t))$$ is connected.
$$\alpha$$-$$C3$$, $$\alpha$$-$$C4$$ and $$S$$-$$C4$$ are preserved under continuous functions. $$\alpha$$-$$C3$$, $$\alpha$$-$$C4$$, $$S$$-$$C4$$ and $$\alpha$$-$$C$$ are good extensions. A non-empty product space is $$\alpha$$-$$C3$$ (resp. $$\alpha$$-$$C4$$ or $$S$$-$$C4$$) iff each factor space is $$\alpha$$-$$C3$$ (resp. $$\alpha$$-$$C4$$ or $$S$$-$$C4$$). Various concepts of fuzzy connectedness are compared. Many examples are given.

### MSC:

 54A40 Fuzzy topology

### Keywords:

fuzzy connectedness
Full Text:

### References:

  Azad, K. K., On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity, J. Math. Anal. Appl., 82, 14-32 (1981) · Zbl 0511.54006  Ali, D. M.; Srivastava, A. K., On fuzzy connectedness, Fuzzy Sets and Systems, 28, 203-208 (1988) · Zbl 0657.54004  Chang, C. L., Fuzzy topological spaces, J. Math. Anal. Appl., 24, 182-190 (1968) · Zbl 0167.51001  Hutton, B., Products of fuzzy topological spaces, Topology Appl., 11, 59-67 (1980) · Zbl 0422.54006  Lowen, R., Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl., 56, 621-633 (1976) · Zbl 0342.54003  Lowen, R., Connectedness in fuzzy topological spaces, Rocky Mountain J. Math., 11, 427-433 (1981) · Zbl 0487.54007  Lowen, R., On the Existence of Natural Non-Topological Fuzzy Topological Spaces (1985), Heldermann: Heldermann Berlin · Zbl 0568.54007  Lowen, R.; Srivastava, A. K., On Preuss’ connectedness concept in FTS, J. Math. Anal. Appl., 127, 151-154 (1987)  Martin, H. W., A Stone-Cěch ultra-fuzzy compactification, J. Math. Anal. Appl., 73, 453-456 (1980) · Zbl 0442.54007  Pu, P. M.; Liu, Y. M., Fuzzy topology I. Neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl., 76, 571-599 (1980) · Zbl 0447.54006  Rodabaugh, S. E., Connectivity and the L-fuzzy unit interval, Rocky Mountain J. Math., 12, 113-121 (1982) · Zbl 0508.54003  Srivastava, R., Topics in fuzzy topology, (Ph.D. Thesis (1983), B.H.U. Varanasi)  Warren, R. H., Convergence in fuzzy topology, Rocky Mountain J. Math., 13, 31-36 (1983) · Zbl 0522.54005  Zheng, C. Y., Fuzzy path and fuzzy connectedness, Fuzzy Sets and Systems, 14, 273-280 (1984) · Zbl 0555.54005
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