Three New Weaker Notions of Fuzzy Open Sets and Related Covering Conceps

Samer H. Al Ghour

Abstract


A subset A of an ordinary topological space (X,T) is ω-open <cite>Hdeib1</cite> (resp. N-open <cite>alomari3</cite>) if for each x∈A, there exists U∈T such that x∈U and U-A is countable (resp. finite). In this work, we extend ω-open and N-open notions to include L-topological spaces, where L is an F-lattice, and we introduce a third notion of L-sets weaker than both of them. For a given L-topological space, the new notions give us three new finer L-topological spaces, which can help us to increase our understanding of this L-topological space. By means of these new notions in L-topological spaces, several types Chang's compactness, and Wong's Lindelöfness will be introduced. We make many comparisons between the new notions, and between these notions and some other related concepts. Several characterizations of the new concepts are given and two characterizations of Wong's Lindelöfness concept are given.

Keywords


Fuzzy compactness; fuzzy Lindelofness; -topology; Q-neighborhood; -open sets.

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References


Al Ghour, S. (2006). Some generalizations of paracompactness.

Missouri Journal of Mathematical Sciences, 18(1):64-77. doi:

1155/2007/16292

Al-Hawary, T. & Al-Omari, A. (2006a). De compositions of continuity. Turkish Journal of Math ematics, 30(2):187195.

Al-Hawary, T. & Al-Omari, A. (2006b). Be tween open and -open

sets. Questions Answers General Topology, 24(2):67-78.

Al-Hawary, T. (2008). Fuzzy -open sets. Bul letin of the Korean

Mathematical Society, 45(4):749-755.

Al-Omari, A. & Noorani, M.S.M. (2007a). Regular generalized

-closed sets. International Journal of Mathematics and Mathematical

Sci ences, Volume 2007: Article ID 16292. doi: 10.1155/2007/16292

Al-Omari, A. & Noorani, M.S.M. (2007b). Contra- -continuous

and almost contra- -continuous. International Journal of Mathematics and Mathematical Sciences, Volume 2007: Article ID 40469. doi:10.1155/2007/40469

Al-Omari, A., Noiri, T. & Noorani, M.S.M. (2009a). Characterizations

of strongly compact spaces. International Journal of Mathematics

and Mathematical Sciences, Volume 2009: Article ID 573038. doi:

1155/2009/573038

Al-Omari, A., Noiri, T. & Noorani, M.S.M. (2009b). Weak and strong

forms of -continuous functions. International Journal of Mathematics

and Mathematical Sciences, Volume 2009: Article ID 174042. doi:

1155/2009/174042

Al-Omari, A. & Noorani, M.S.M. (2009). New topology and

characterization of compact spaces. Proceedings of the 5th Asian

Mathematical Con ference. The Putra World Trade Center, Kuala

Lumpur, Malaysia.

Al-Zoubi, K.Y. (2005). On generalized - closed sets. International

Journal of Mathematics and Mathematical Sciences, 13:2011-2021.

Azad, K.K. (1981). On fuzzy semicontinuity, fuzzy almost continuity

and fuzzy weakly continuity. Journal of Mathematical Analysis and

Applications, 82(1):14-32.

Aygn, H. (2000). -compactness in -fuzzy topological spaces.

Fuzzy Sets and Systems, 116(3):317-324. doi: 10.1016/S0165-

(98)00345 5

Chang, C.L. (1968). Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 24:182-190.

Chauhan, S., Kutukcu, S., Dhiman, N. & Ku mar, S. (2014).

Variants of R-weakly commuting mappings and common fixed point

theorems in in tuitionistic fuzzy metric spaces. Kuwait Journal of

Science, 41(2):49-64.

Cho, S.H. & Lee, G.Y. (2005). A note on regu lar semiopen L-sets and S*-closed spaces. Fuzzy Sets and Systems, 149(3):493-500.

Dang, S., Behera, A. & Nanda, S. (1994). On fuzzy weakly semicontinuous functions. Fuzzy Sets and Systems, 67(2):239-245. doi:10.1016/0165 0114(94)90091-4

Davvaz, B. & Leoreanu-Fotea, V. (2014). Triangular fuzzy sub

?-semihypergroups in ?-semihypergroups. Kuwait Journal of Science, 41(1):93-106.

Davvaz, B. & Hassani Sadrabadi, E. (2014). On Atanassovs

intuitionistic fuzzy grade of the di rect product of two hypergroupoids. Kuwait Journal of Science, 41(3):47-61.

Et, M., Tripathy, B.C. & Dutta, A.J. (2014). On pointwise statistical

convergence of order of sequences of fuzzy mappings. Kuwait Journal of Sci ence, 41(3):17-30.

Fora, A.A. (1989). Separation axioms for fuzzy spaces. Fuzzy Sets and Systems, 33(1):59-75. doi: 10.1016/0165-0114(89)90217-0

Ganguly, S. & Saha, S. (1986). A note on semi-open sets in fuzzy

topological spaces. Fuzzy Sets and Systems, 18(1):83-96. doi:

1016/0165 0114(86)90029-1

Ghosh, B. (1990). Semi-continuous and semi-closed mappings

and semi-connectedness in fuzzy setting. Fuzzy Sets and Systems,

(3):345-355. doi: 10.1016/0165-0114(90)90008-T

Hdeib, H.Z. (1982). -closed mappings. Revista Colombiana de

Mathematicas, 16(1-2):65-78.

Hdeib, H.Z. (1989). -continuous functions. Di rasat Journal 16:136-

Hhle, U. (1991). Special memorial volume second issue:

mathematical aspects of fuzzy set the ory. Fuzzy Sets and Systems,

(2):253-407.

Hhle, U., Rodabaugh, S.E. & ostak, A. (1995). Special issue on

fuzzy topology. Fuzzy Sets and Systems, 73(1):1183.

Hhle, U. & ostak, A. (1999). Axiomatic foun dations of fixed-basis

fuzzy topology. In: Hhle, U. & Rodabaugh, S. E. (Ed.). Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory. The Hand books of Fuzzy Sets Series. Pp. 123-273. Kluwer Academic Publishers, Dordrecht.

Hhle, U. (2001). Many valued topology and its applications. Kluwer

Academic Publishers, Boston. Pp. 382.

Liu, Y.M. & Luo, M.K. (1997). Fuzzy topology. World Scientific

Publishing, Singapore. Pp. 353.

Mukherjee, M.N. & Sinha, S.P. (1989a). Irres olute and almost open

functions between fuzzy topo logical spaces. Fuzzy Sets and Systems,29(3):381-388. doi: 10.1016/0165-0114(89)90050-X

Mukherjee, M.N. & Sinha, S.P. (1989b). On some weaker forms

of fuzzy continuous and fuzzy open mappings on fuzzy topological

spaces. Fuzzy Sets and Systems, 32(1):103-114. doi: 10.1016/0165-0114(89)90091-2

Mukherjee, A. (1999). Fuzzy totally continuous and totally semi continuous functions. Fuzzy Sets and Systems, 107(2):227-230. doi: 10.1016/S0165 0114(97)00320-5

Pant, B.D., Chauhan, S., Cho, Y.J. & Eshaghi-Gordji, M. (2015).

Fixed points of weakly compatible mappings in fuzzy metric spaces.

Kuwait Journal of Science, 42(2):107-127.

Rodabaugh, S.E., Klement, E.P. & Hhle, U. (1992). Applications

of category theory to fuzzy subsets. Kluwer Academic Publishers,

Dordrecht. Pp. 398.

Rodabaugh, S.E. & Klement, E.P. (2003). Topological and algebraic

structures in fuzzy sets: A handbook of recent developments in the

Mathe matics of fuzzy sets. Kluwer Academic Publishers, Dordrecht.

Pp. 467.

Sarsak, M.S. (2003). -almost Lindelf spaces. Questions Answers

General Topology, 21(1):2735.

Sen, M. & Roy, S. (2013). On paranormed type fuzzy I-convergent

double multiplier sequences. Kuwait Journal of Science, 40(1):1-12.

Wang, G.J. (1988). Theory of L-Fuzzy topological spaces. Shaanxi

Normal University Press, Xian (in Chinese).

Wong, C.K. (1973). Covering properties of fuzzy topological spaces.

Journal of Mathematical Analysis and Applications, 43:697-704.

Zulfiqar, M. (2014). Characterizations of ( )-fuzzy fantastic

ideals in BCI-algebras. Kuwait Journal of Science, 41(1):35-64.

Zulfiqar, M. & Shabir, M. (2015). Characterizations of

-interval valued fuzzy H-ideals in BCK-algebras. Kuwait Journal of

Science, 42(2):42-66.


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