## On extensions of fuzzy topologies.(English)Zbl 0795.54011

Summary: We introduce the concept of extension of fuzzy topologies. If $$(X,T)$$ is a fuzzy topological space having the property ‘$$P$$’ we find conditions under which the extension of $$T$$ will also have the same property ‘$$P$$’.

### MSC:

 54A40 Fuzzy topology 54D35 Extensions of spaces (compactifications, supercompactifications, completions, etc.)
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### References:

 [1] C. J.R. Borges: On extensions of topologies. Canad. J. Math. 19 (1967), 148-151. · Zbl 0167.20801 [2] C. L. Chang: Fuzzy topological spaces. J. Math. Anal. Appl. 24 (1968), 182-201. · Zbl 0167.51001 [3] U. V. Fatteh, D.S. Bassan: Fuzzy connectedness and its stronger forms. J. Math. Anal. Appl. 111 (1985), 449-464. · Zbl 0588.54008 [4] B.W. Hutton, I.L. Reilly: Separation axioms in fuzzy topological spaces. Fuzzy Sets and Systems 3 (1980), 99-104. · Zbl 0421.54006 [5] R. Lowen: Fuzzy topological spaces and fuzzy compactness. J. Math. Anal. Appl. 56 (1976), 621-633. · Zbl 0342.54003 [6] R. Lowen: A comparison of different compactness notions in fuzzy topological spaces. J. Math. Appl. 64 (1978), 446-454. · Zbl 0381.54004 [7] N. Levine: Simple extensions of topologies. Amer. Math. Monthly 11 (1964), 22-25. · Zbl 0121.17203 [8] R. Srivastava S.N. Lal, A.K. Srivastava: Fuzzy Hausdorff topological spaces. J. Math. Anal. Appl. 81 (1981), 497-506. · Zbl 0491.54004 [9] R. Srivastava S. N. Lal, A. K. Srivastava: On fuzzy $$T_{1}$$-topological spaces. J. Math. Anal. Appl. 136 (1988), 124-130. · Zbl 0687.54007
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