#### Abstract:

*In this paper, we introduce two notions of * * property in fuzzy topological spaces by using quasi-coincidence sense and we establish relationship among our and others such notions. We also show that all these notations satisfy good extension property. Also hereditary, productive and projective properties are satisfied by these notions. We observe that all these concepts are preserved under one-one, onto, fuzzy open and fuzzy continuous mappings. Finally, we discuss initial and final fuzzy topologies on our second notion.*#### Keywords:

Fuzzy Topological Space,Quasi-coincidence,Fuzzy T

_{1} Topological Space,Good Extension,

#### Refference:

1) Ali, D. M. On certain separation and connectedness concepts in fuzzy topology, PhD, Banaras Hindu University, India, 1990.

2) Amin,M. R. Ali, D. M. and Hossain, M. S. On fuzzy bitopological spaces, Journal of Bangladesh Academy of Sciences, 32(2) (2014) 209- 217.

3) Amin,M. R. Ali, D. M. and Hossain, M. S. Concepts in fuzzy bitopological spaces, Journal of Mathematical and Computational Sciences, 4(6) (2014) 1055-1063.

4) Amin,M. R. and Hossain, M. S. On concepts in fuzzy bitopological spaces, Anals of Fuzzy Mathematics and Informatics, 11(6) (2016) 945- 955.

5) Chang, C. L. Fuzzy topological spaces, J. Math. Anal. Appl. 24(1968), 182

192.

6) Ahmd, Fora. Ali Separations axioms for fuzzy spaces, Fuzzy Sets and Systems, 33(1989), 59-75.

7) Goguen, T. A. Fuzzy Tychonoff theorem, J. Math. Anal. Appl. 43(1973), 734-742.

8) Guler, A. C. Kale Goknur, Regularity and normality in soft ideal topological spaces, Anals of Fuzzy Mathematics and Informatics, 9(3) (2015), 373-383.

9) Hossain, M. S. and Ali, D. M. On T1 fuzzy bitopological spaces, J. Bangladesh Acad. Sci., 31(2007), 129-135.

10) Hutton, B. Normality in fuzzy topological spaces, J. Math. Anal. Appl. 50(1975), 74-79.

11) Kandil and El-Shafee: Separation axioms for fuzzy bitopological spaces, J. Inst. Math. Comput. Sci. 4(3)(1991), 373-383.

12) Lipschutz, S. General topology, Copyright 1965, by the Schaum publishing company.

13) Lowen, R. Fuzzy topological spaces and fuzzy compactness, J. Math. Anal. Appl. 56(1976), 621-633.

14) Lowen, R. Initial and final fuzzy topologies and the fuzzy Tyconoff theorem, J. Math. Anal. Appl. 58(1977), 11-21.

15) Malghan, S. R. and Benchalli, S. S. On open maps, closed maps and local compactness in fuzzy topological spaces, J. Math. Anal. Appl. 99(2)(1984), 338-349.

16) Ming Pu. Pao. and Ming, Liu Ying. Fuzzy topology I. neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76(1980), 571-599.

17) Ming Pu. Pao. and Ming, Liu Ying.Fuzzy topology II. product and quotient spaces, J. Math. Anal. Appl. 77(1980), 20-37.

18) Rudin,W. Real and Complex Analysis, Copyright 1966, by McGraw Hill Inc.

19) Miah Saikh Shahjahan and Amin, Md Ruhul. Mappings in fuzzy Hausdorff spaces in quasi-coincidence sense, Journal of Bangladesh Academy of Sciences, (accepted).

20) Miah Saikh Shahjahan and Amin, M. R. Certain properties on fuzzy R0 topological spaces in quasi-coincidence sense, Annals of Pure and Applied, (accepted).

21) Srivastava, R. Lal S. N. and Srivastava, A. K. On fuzzy and topological spaces, J. Math. Anal. Appl. 136 (1988), 66-73.

22) Warren, R. H. Continuity of mappings in fuzzy topological spaces, Notices A.M. S. 21(1974), A-451.

23) Wong, C. K. Fuzzy topology: product and quotient theorem, J. Math. Anal. Appl. 45(1974), 512-521.

24) Wuyts, P. and Lowen, R. On separation axioms in fuzzy topological spaces, fuzzy neighborhood spaces, and fuzzy uniform spaces, J. Math. Anal. Appl. 93(1983), 27-41.

25) Zadeh, L. A. Fuzzy sets, Information and control, 8(1965), 338-353.

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