## Fuzzy connectedness and its stronger forms.(English)Zbl 0588.54008

A topological space is said to be superconnected if each nonempty open subset is dense, and strongly connected if it is not the union of two nonempty proper open subsets. The authors study the analogues of ordinary connectedness and these two strong forms of connectedness in fuzzy topological spaces. Many elementary theorems on connectedness hold in the setting of fuzzy spaces, but some do not. For example, the fuzzy product of fuzzy connected spaces need not be fuzzy connected. The paper contains a very nice introduction to fuzzy sets and fuzzy topological spaces.
Reviewer: B.J.Pearson

### MSC:

 54A40 Fuzzy topology 54D05 Connected and locally connected spaces (general aspects)
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### References:

 [1] Zadeh, L.A, Fuzzy sets, Inform. and control, 8, 338-353, (1965) · Zbl 0139.24606 [2] Chang, C.L, Fuzzy topological spaces, J. math. anal. appl., 24, 182-190, (1968) · Zbl 0167.51001 [3] Wong, C.K, Fuzzy topology: product and quotient theorems, J. math. anal. appl., 45, 512-521, (1974) · Zbl 0273.54002 [4] Levine, N, Dense topologies, Amer. math. monthly, 75, 847-852, (1968) · Zbl 0197.19002 [5] Levine, N, Strongly connected sets in a topology, Amer. math. monthly, 72, No. 10, 1099-1101, (1965) · Zbl 0134.42105 [6] Warren, R.H, Neighborhoods, bases, and continuity in fuzzy topological spaces, Rocky mountain J. math., 8, 459-470, (1978) · Zbl 0394.54003 [7] {\scK. K. Azad}, On fuzzy semi-continuity, fuzzy almost continuity, and fuzzy Weak continuity, J. Math. Anal. Appl., to appear. · Zbl 0511.54006 [8] {\scK. K. Azad}, Fuzzy connectedness, unpublished. [9] {\scU. V. Fatteh and D. S. Bassan}, A note on D-spaces, Bull. Calcutta Math. Soc.{\bf75}(6). · Zbl 0501.54017
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