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ω-Convergence theory of filters in Lω -spaces

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Abstract

In this paper, an ω-convergence theory of filters in an Lω-space is established. By means of the ω-convergence theory, some important characterizations with respective to the ω-closed sets, ω T 2 separation and (ω 1, ω 2)-continuous mappings are obtained. Moreover, the mutual relationships among ω-convergence of molecular nets, ω-convergence of ideals and ω-convergence of filters are given.

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References

  • Chen, S.-L. (1992). Moore-Smith θ-convergence theory on completely distributive lattices. In Proc. Fuzzy Math. and Systems, Hunan Science and Technology Press, Changsha, China. (pp. 34–36).

  • Chen S.-L. (1993) θ-Convergence theory of ideals on completely distributive lattices. Journal of Mathematics 13(2): 47–52

    Google Scholar 

  • Chen S.-L., Chen S.-L., Wang X.-G. (2004) σ-Convergence theory and its applications in fuzzy lattices. Information Sciences 165: 45–58

    Article  MATH  MathSciNet  Google Scholar 

  • Chen S.-L., Chen S.-T. (2000) A new extension of fuzzy convergence. Fuzzy Sets and Systems 109: 199–204

    Article  MATH  MathSciNet  Google Scholar 

  • Chen S.-L. (1995a) Urysohn-convergence of fuzzy ideals. Journal Fuzzy Mathematics 3(3): 555–558

    MATH  Google Scholar 

  • Chen S.-L., Cheng J.-S. (1997) θ-Convergence of nets of L-fuzzy sets and its applications. Fuzzy Sets and Systems 86: 235–240

    Article  MATH  MathSciNet  Google Scholar 

  • Chen S.-L., Zhou W.-N. (1999) SU-separation axioms in topological molecular lattices. Journal Fuzzy Mathematics 7(4): 987–995

    MATH  MathSciNet  Google Scholar 

  • Chen S.-L., Wu J.-R. (1999) σ-Convergence theory of ideals in fuzzy lattices. Journal Wuhan Urban Construction Institute 16(4): 43–47

    Google Scholar 

  • Chen S.-L., Wang X.-G. (2000) Sθ-convergence theory in L-fuzzy topology. Journal Fuzzy Mathematics 8(2): 501–516

    MATH  Google Scholar 

  • Chen S.-L., Wu J.-R. (2000) SR-convergence theory in fuzzy lattices. Information Sciences 125: 233–247

    Article  MATH  MathSciNet  Google Scholar 

  • Chen, S.-L., Cheng, J.-S. (1993). Theory of R-convergence of ideals on fuzzy lattices and its applications. In Proceeding of the Fifth IFSA World Congress, pp. 269–273, Vol. I, Korea.

  • Chen S.-L. (1995b) U-convergence and L-fuzzy U-sets. Information Sciences 87(4): 205–213

    Article  MATH  MathSciNet  Google Scholar 

  • Chen S.-L. (2000) σ-Convergence of molecular nets in fuzzy lattices. Fuzzy Systems and Mathematics 14(1): 13–18

    MathSciNet  Google Scholar 

  • Chen, S.-L., Cheng, J.-S. (2005). On Lω-spaces. In Proceedings of the Eleventh IFSA Word Congress, Vol. I, pp. 257–261,Tsinghua University Press.

  • Chen S.-L., Dong C.-Q. (2002) L-order-preserving operator spaces. Fuzzy Systems and Mathematics 16(ZJ): 36–41

    Google Scholar 

  • Chen S.-L. (2002) Moore-Smith convergence theory on L-fuzzy order-preserving operator spaces. Journal Jimei University 7(3): 271–277

    Google Scholar 

  • Chen S.-L. (2006) On L-fuzzy order-preserving operator ω-spaces. Journal Fuzzy Mathematics 14(2): 481–498

    MATH  Google Scholar 

  • Huang Z.-X., Chen S.-L. (2005) ω-separation axioms in Lω-space. Journal Mathematics 25(4): 383–388

    MATH  MathSciNet  Google Scholar 

  • Hutton B. (1977) Uniformities on fuzzy topological spaces. Journal Mathematical Analysis and Applications 58: 559–571

    Article  MATH  MathSciNet  Google Scholar 

  • Lowen R. (1983) Relation between filter and net convergence in fuzzy topological spaces. Fuzzy Mathematics 4: 41–52

    MathSciNet  Google Scholar 

  • Pu P.-M., Liu Y.-M. (1980) Fuzzy topology I: Neighborhood structure of a fuzzy point and Moore-Smith convergence. Journal Mathematics Analysis and Applications 76: 57–599

    MathSciNet  Google Scholar 

  • Wang G.-J. (1983) A new fuzzy compactness defined by fuzzy nets. Journal Mathematics Analysis and Applications 94: 1–23

    Article  MATH  Google Scholar 

  • Wang G.-J. (1992) Theory of topological molecular lattices. Fuzzy Sets and Systems 47: 351–376

    Article  MATH  MathSciNet  Google Scholar 

  • Wu K. (2000) Convergences of fuzzy sets based on decomposition theory and fuzzy polynomial function. Fuzzy Sets and Systems 109(2): 173–186

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Science, Jimei University, Xiamen, Fujian, 361021, People’s Republic of China

    Shui-Li Chen

  2. College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian, 350002, People’s Republic of China

    Guo-Long Chen

  3. Department of Mathematics, Quanzhou Normal University, Quanzhou, Fujian, 362000, People’s Republic of China

    Jian-Cheng Zhang

Authors
  1. Shui-Li Chen
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  2. Guo-Long Chen
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  3. Jian-Cheng Zhang
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Correspondence to Shui-Li Chen.

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Chen, SL., Chen, GL. & Zhang, JC. ω-Convergence theory of filters in Lω -spaces. Fuzzy Optim Decis Making 7, 351–360 (2008). https://doi.org/10.1007/s10700-008-9043-0

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