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On a topological universe of L-bornological spaces

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Abstract

This paper shows that given a certain frame L, the construct of strict L-bornological spaces, introduced by Abel and Šostak, is a topological universe.

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References

  • Abel M, Šostak A (2011) Towards the theory of \(L\)-bornological spaces. Iran J Fuzzy Syst 8(1):19–28

    MathSciNet  MATH  Google Scholar 

  • Adámek J, Herrlich H, Strecker GE (2009) Abstract and concrete categories: the joy of cats. Dover Publications, New York

    MATH  Google Scholar 

  • Birkhoff G (1979) Lattice theory, 3rd edn. American Mathematical Society Colloquium Publications, vol. XXV. American Mathematical Society

  • Engelking R (1989) General topology. Heldermann Verlag

  • Gierz G, Hofmann KH et al (2003) Continuous lattices and domains. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  • Hermann P, Mrkvička T, Mattfeldt T, Minárová M, Helisová K, Nicolis O, Wartner F, Stehlík M (2015) Fractal and stochastic geometry inference for breast cancer: a case study with random fractal models and Quermass-interaction process. Stat Med 34(18):2636–2661

    Article  MathSciNet  Google Scholar 

  • Hogbe-Nlend H (1977) Bornologies and functional analysis. Mathematics Studies, vol. 26. North-Holland Publishing Company

  • Höhle U, Šostak AP (1999) Axiomatic foundations of fixed-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 123–272

  • Jäger G (2001) A category of \(L\)-fuzzy convergence spaces. Quaest Math 24(4):501–517

    Article  MathSciNet  MATH  Google Scholar 

  • Johnstone PT (1982) Stone spaces. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Liu YM, Luo MK (1997) Fuzzy topology. World Scientific Publishing Co

  • Paseka J, Solovyov S, Stehlík M (2015) Lattice-valued bornological systems. Fuzzy Sets Syst 259:68–88

  • Rodabaugh SE (1999) Categorical foundations of variable-basis fuzzy topology. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 273–388

  • Rodabaugh SE (1999) Powerset operator foundations for poslat fuzzy set theories and topologies. In: Höhle U, Rodabaugh SE (eds) Mathematics of Fuzzy Sets: Logic, Topology and Measure Theory. Kluwer Academic Publishers, pp 91–116

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Acknowledgments

This research was supported by the ESF Project No. CZ.1.07/2.3.00/20.0051 “Algebraic methods in Quantum Logic” of the Masaryk University in Brno, Czech Republic; and also by the Aktion Project No. 67p5 (Austria–Czech Republic) “Algebraic, fuzzy and logical aspects of statistical learning for cancer risk assessment”. M. Stehlík was additionally supported by Fondecyt Proyecto Regular No. 1151441. Last but not least, the authors are very grateful to the editor and the reviewers for their valuable comments.

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Correspondence to Sergey A. Solovyov.

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The authors declare that there is no conflict of interests regarding the publication of this paper.

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Communicated by A. Di Nola.

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Paseka, J., Solovyov, S.A. & Stehlík, M. On a topological universe of L-bornological spaces. Soft Comput 20, 2503–2512 (2016). https://doi.org/10.1007/s00500-015-1905-0

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  • DOI: https://doi.org/10.1007/s00500-015-1905-0

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