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Epireflections in the category of \(T_{0}\) stratified Q-cotopological spaces

Soft Computing volume 27, pages 2443–2451 (2023)Cite this article

Abstract

In this paper, we show that the category SobQ-CTop of all sober Q-cotopological spaces is the epireflective subcategory of \({{\textbf {S}}}Q{\text {-}}{{\textbf {CTop}}}_{0}\) of all \(T_{0}\) stratified Q-cotopological spaces. In particular, we mainly prove that \({{\textbf {Sob}}}Q{\text {-}}{{\textbf {CTop}}}\) is the epireflective hull of Sierpinski Q-cotopological space \(Q_{S}\) in \({{\textbf {S}}}Q{\text {-}}{{\textbf {CTop}}}_{0}\), where Q is the unit interval endowed with a left continuous t-norm.

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References

  • Adámek J, Herrlich H, Strecker G (1990) Abstract and concrete categories: the joy of cats. Wiley, New York

    MATH  Google Scholar 

  • Brümmer GCL, Giuli E, Herrlich H (1992) Epireflections which are completions. Cahiers de Topologie et Géométrie Différentielle Catégoriques 33:71–93

    MathSciNet  MATH  Google Scholar 

  • Bělohlávek R (2002) Fuzzy relational systems: foundations and principles. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Chen PW, Zhang DX (2010) Alexandroff L-co-topological spaces. Fuzzy Sets Syst 161(18):2505–2514

    Article  MathSciNet  MATH  Google Scholar 

  • Fan L (2001) A new approach to quantitative domain theory. Electron Notes Theor Comput Sci 45:77–87

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Klement EP, Mesiar R, Pap E (2000) Triangular Norms. Kluwer Academic Publishers, Dordrecht

    Book  MATH  Google Scholar 

  • Lai HL, Zhang DX (2007) Complete and directed complete \(\omega \)-categories. Theor Comput Sci 388:1–25

    Article  MathSciNet  MATH  Google Scholar 

  • Manes EG (1974) Compact Hausdorff objects. Gen Topol Appl 4:341–360

    Article  MathSciNet  MATH  Google Scholar 

  • Nel DL, Wilson RG (1972) Epireflections in the category of T\(_{0}\) spaces. Fundamenta Mathematicae 75:69–74

    Article  MathSciNet  MATH  Google Scholar 

  • Noor R, Srivastava AK (2014) The categories L-Top\(_{0}\) and L-Sob as epireflective hulls. Soft Comput 18:1865–1871

    Article  MATH  Google Scholar 

  • Rosenthal KI (1990) Quantales and Their applications. Longman Scientific and Technical, New York

    MATH  Google Scholar 

  • Scott DS (1970) Outline of a mathematical theory of computation, in: The 4th annual princeton conference on information sciences and systems. Princeton University Press, Princeton, NJ

  • Singh SK, Srivastava AK (2016) On Q-sobriety. Quaestiones Mathematicae 39:179–188

    Article  MathSciNet  MATH  Google Scholar 

  • Srivastava AK, Khastgir AS (1998) On fuzzy sobriety. Inf Sci 110:195–205

    Article  MathSciNet  MATH  Google Scholar 

  • Yao W (2012) A survey of fuzzifications of frames, the papert-papert-isbell adjunction and sobriety. Fuzzy Sets Syst 190:63–81

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang DX (2018) Sobriety of quantale-valued cotopological spaces. Fuzzy Sets Syst 350:1–19

  • Zhang QY, Fan L (2005) Continuity in quantitative domains. Fuzzy Sets Syst 154:118–131

  • Zhang YJ, Wang KY (2019) Bounnded sobriety and k-bounded sobriety of Q-cotopological spaces. Filomat 33(7):2095–2106

    Article  MathSciNet  MATH  Google Scholar 

  • Zhang ZX, Shi FG, Li QG, Wang K (2021) On fuzzy monotone convergence Q-cotopological spaces. Fuzzy Sets Syst 425:18–33

    Article  MathSciNet  Google Scholar 

Download references

Funding

This research is supported by a grant of National Natural Science Foundation of China (11531009).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi’an, 710119, People’s Republic of China

    Bin Zhao & Yujing Zhang

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  1. Bin Zhao
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  2. Yujing Zhang
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Contributions

BZ helped in formal analysis, writing—original draft, conceptualization, writing—review & editing, methodology, supervision. YZ contributed to visualization, writing—original draft, formal analysis, writing—review & editing, methodology, validation.

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Correspondence to Yujing Zhang.

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Zhao, B., Zhang, Y. Epireflections in the category of \(T_{0}\) stratified Q-cotopological spaces. Soft Comput 27, 2443–2451 (2023). https://doi.org/10.1007/s00500-022-07809-y

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  • DOI: https://doi.org/10.1007/s00500-022-07809-y

Keywords

  • Epireflective hull
  • Sobriety
  • Q-cotopological space
  • Sierpinski Q-cotopological space