# WEAK SMOOTH α-STRUCTURE OF SMOOTH TOPOLOGICAL SPACES

Park, Chun-Kee;Min, Won-Keun;Kim, Myeong-Hwan

• Published : 2004.01.01
• 49 9

#### Abstract

In [3] and [6] the concepts of smooth closure, smooth interior, smooth ${\alpha}-closure$ and smooth ${\alpha}-interior$ of a fuzzy set were introduced and some of their properties were obtained. In this paper, we introduce the concepts of several types of weak smooth compactness and weak smooth ${\alpha}-compactness$ in terms of these concepts introduced in [3] and [61 and investigate some of their properties.

#### Keywords

fuzzy sets;smooth topology;${\alpha}-closure$;${\alpha}-interior$;weak smooth compactness;weak smooth ${\alpha}-compactness$

#### References

1. Fuzzy Sets and Systems v.90 On several types of compactness in smooth topological spaces M.Demirci https://doi.org/10.1016/S0165-0114(96)00121-2
2. Fuzzy Sets and Systems v.48 Smooth topological spaces A.A.Ramadan https://doi.org/10.1016/0165-0114(92)90352-5
3. J. Math. Anal. Appl. v.24 Fuzzy topological spaces C.L.Chang https://doi.org/10.1016/0022-247X(68)90057-7
4. Inform. and Control v.8 Fuzzy sets L.A.Zadeh https://doi.org/10.1016/S0019-9958(65)90241-X
5. Fuzzy Sets and Systems v.62 Almost compactness and near compactness in smooth topological spaces M.K.El Gayyar;E.E.Kerre;A.A.Ramadan https://doi.org/10.1016/0165-0114(94)90059-0
6. First IFSA Congress Smooth axiomatics R.Badard
7. Int. J. Math. Sci. 2003 no.46 α-compactness in smooth topological spaces C.K.Park;W.K.Min;M.H.Kim https://doi.org/10.1155/S0161171203303035
8. Fuzzy Sets and Systems v.101 Three toplogical structures of smooth topological spaces M.Demirci https://doi.org/10.1016/S0165-0114(97)00117-6

#### Cited by

1. Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces vol.33, pp.2, 1996, https://doi.org/10.1007/BF02093505
2. Coincidence theorems for set-valued mappings and Ekeland's variational principle in fuzzy metric spaces vol.79, pp.2, 1996, https://doi.org/10.1016/0165-0114(95)00084-4
3. Coincidence point theorems in generating spaces of quasi-metric family vol.116, pp.3, 2000, https://doi.org/10.1016/S0165-0114(98)00469-2
4. Ekeland's variational principle and Caristi's coincidence theorem for set-valued mappings in probabilistic metric spaces vol.14, pp.7, 1993, https://doi.org/10.1007/BF02455381