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Some notes on soft topological spaces

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Abstract

The first aim of this study is to define soft topological spaces and to define soft continuity of soft mappings. Second is to introduce soft product topology and study properties of soft projection mappings. Third is to define soft compactness and generalize Alexander subbase theorem and Tychonoff theorem to the soft topological spaces.

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References

  1. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  2. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 64(2):87–96

    Article  Google Scholar 

  3. Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11:341–356

    Article  MathSciNet  MATH  Google Scholar 

  4. Molodtsov D (1999) Soft set theory-First results. Comput Math Appl 37(4/5):19–31

    Article  MathSciNet  MATH  Google Scholar 

  5. Maji PK, Roy AR, Biswas R (2002) An application of soft set in decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  6. Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418

    Article  MATH  Google Scholar 

  7. Aktaş H, Çağman N (2007) Soft sets and soft group. Inf Sci 177:2726–2735

    Article  MATH  Google Scholar 

  8. Jun YB (2008) Soft BCK/BCI-algebras. Comput Math Appl 56((5):1408–1413

    Article  MathSciNet  MATH  Google Scholar 

  9. Jun YB, Park CH (2008) Applications of soft sets in ideal theory of BCK/BCI-algebras. Inf Sci 178(11):2466–2475

    MathSciNet  MATH  Google Scholar 

  10. Jun YB, Lee KJ, Park CH (2009) Soft set theory applied to ideals in d-algebras. Comput Math Appl 57(3):367–378

    Article  MathSciNet  MATH  Google Scholar 

  11. Jun YB, Lee KJ, Zhan J (2009) Soft p-ideals of soft BCI-algebras. Comput Math Appl 58(10):2060–2068

    Article  MathSciNet  MATH  Google Scholar 

  12. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56(10):2621–2628

    Article  MathSciNet  MATH  Google Scholar 

  13. Sun QM, Zhang ZL, Liu J (2008) Soft sets and soft modules. In: Wang G, Li T, Grzymala-Busse JW, Miao D, Skowron A, Yao Y (eds) Proceedings of the third international conference on rough sets and knowledge technology, RSKT 2008, Lecture Notes in Computer Science, vol 5009, Springer, pp 403–409

  14. Aygünoğlu A, Aygün H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58:1279–1286

    Article  MathSciNet  MATH  Google Scholar 

  15. Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24:182–190

    Article  MathSciNet  MATH  Google Scholar 

  16. Lowen R (1976) Fuzzy topological spaces and fuzzy compactness. J Math Anal Appl 56:621–633

    Article  MathSciNet  MATH  Google Scholar 

  17. Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562

    Article  MathSciNet  MATH  Google Scholar 

  18. Majumdar P, Samanta SK (2008) Similarity measure of soft set. New Math Nat Comput 4(1):1–12

    Article  MathSciNet  MATH  Google Scholar 

  19. Çağman N, Enginoğlu S (2010) Soft set theory and uni-int decision making. Eur J Oper Res 207:848–855

    Article  MATH  Google Scholar 

  20. Kharal A, Ahmad B, Mappings on Soft Classes, to appear in New Mathematics and Natural Computation

  21. Babitha KV, Sunil JJ (2010) Soft set relations and functions. Comput Math Appl 60:1840–1849

    Article  MathSciNet  MATH  Google Scholar 

  22. Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61:1786–1799

    Article  MathSciNet  MATH  Google Scholar 

  23. Adámek J, Herrlich H, Strecker GE (1990) Abstract and concrete categories. Wiley, New York

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Kocaeli, Umuttepe Campus, 41380, Kocaeli, Turkey

    Abdülkadir Aygünoğlu & Halis Aygün

Authors
  1. Abdülkadir Aygünoğlu
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  2. Halis Aygün
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Correspondence to Abdülkadir Aygünoğlu.

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Aygünoğlu, A., Aygün, H. Some notes on soft topological spaces. Neural Comput & Applic 21 (Suppl 1), 113–119 (2012). https://doi.org/10.1007/s00521-011-0722-3

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  • DOI: https://doi.org/10.1007/s00521-011-0722-3

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