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Journals / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 3

Pre-Hausdorff and Hausdorff objects in the category of quantale-valued closure spaces

Muhammad QASIM
Bin PANG
Pages
612–623
Publication Date
2022-10-18
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The main objectives of this paper are to characterize $\overline{T_{0}}$, $T_{0}$, $T_{1}$ and pre-$\overline{T_{2}}$ objects in the category of quantale-valued closure space as well as to examine their mutual relationship.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In previous papers, several $T_{0}$ and Hausdorff objects in topological categories are introduced and compared.
📊
Key Findings & Data:In previous papers, several $T_{0}$ and Hausdorff objects in topological categories are introduced and compared.
💡
Conclusion & Impact:The main objectives of this paper are to characterize $\overline{T_{0}}$, $T_{0}$, $T_{1}$ and pre-$\overline{T_{2}}$ objects in the category of quantale-valued closure space as well as to examine their mutual relationship.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:$\mathcal{V}$-closure space · $\mathcal{V}$-topological space · topological category

Abstract

In previous papers, several $T_{0}$ and Hausdorff objects in topological categories are introduced and compared. The main objectives of this paper are to characterize $\overline{T_{0}}$, $T_{0}$, $T_{1}$ and pre-$\overline{T_{2}}$ objects in the category of quantale-valued closure space as well as to examine their mutual relationship.

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Cite This Article

QASIM, M., PANG, B. (2022). Pre-Hausdorff and Hausdorff objects in the category of quantale-valued closure spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 3, 612–623. https://ajindex.com/articles/529500

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References (24)

  1. J. Adamek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories, John Wiley & Sons, New York, 1990
  2. D. Aerts, Foundations of quantum physics: a general realistic and operational approach, Int. J. Theoret. Phys. 38 (1), 289–358, 1999
  3. D. Aerts, E. Colebunders, A. Van der Voorde and B. Van Steirteghem, State property systems and closure spaces: a study of categorical equivalence, Int. J. Theoret. Phys. 38 (1), 359–385, 1999
  4. G. Aumann, Kontaktrelationen, Bayer. Akad. Wiss. Math.-Nat. Kl. Sitzungsber, 67– 77, 1970
  5. M. Baran, Separation Properties, Indian J. Pure Appl. Math. 23, 333–341, 1991
  6. M. Baran, Separation properties in the categories of Constant Convergence Spaces, Turkish J. Math. 18, 238–248, 1994
  7. M. Baran, Separation Properties in Topological Categories, Math. Balkanica. 10, 39– 48, 1996
  8. M. Baran, $T_{3}$ and $T_{4}$-objects in topological categories, Indian J. Pure Appl. Math. 29, 59–70, 1998
  9. M. Baran, Completely regular objects and normal objects in topological categories, Acta Math. Hungar. 80 (3), 211–224, 1998
  10. M. Baran, Pre $T_{2}$ objects in topological categories, Appl. Categ. Structures, 17, 591– 602, 2009
  11. M. Baran and H. Altındiş, $T_{2}$ objects in topological categories, Acta Math. Hungar. 71 (1-2), 41–48, 1996
  12. M. Baran, D. Tokat and M. Kula, Connectedness and Separation in the Category of Closure Spaces, Filomat 24 (2), 67–79, 2010
  13. G. Birkhoff, Lattice Theory, American Mathematical Society, Providence, Rhonde Island, 1940
  14. E. Čech, On bicompact spaces, Ann. Math. 38, 823–844, 1937
  15. D. Deses, E. Giuli and E. Lowen-Colebunders, On the complete objects in the category of T0 closure spaces, Appl. Gen. Topology, 4, 25–34, 2003
  16. M. Erné, Lattice representations for categories of closure spaces, Categorical Topology, Sigma Series in Pure Mathematics 5, Heldermann Verlag Berlin, 197–222, 1984
  17. R.C. Flagg, Quantales and continuity spaces, Algebra Univers. 37, 257–276, 1997
  18. P. Hertz, Über Axiomensysteme für beliebige Satzsysteme, Teil I, Math. Ann. 87, 246–269, 1922
  19. G. Jäger, Probabilistic Approach Spaces, Math. Bohem. 142 (3), 277–298, 2017
  20. G. Jäger and W. Yao, Quantale-valued gauge spaces, Iran. J. Fuzzy Syst. 15 (1), 103–122, 2018
  21. P.T. Johnstone, Stone Spaces, L. M. S. Mathematics Monograph: No
  22. Academic Press, New York, 1977
  23. M. Kula, A note on Cauchy spaces, Acta Math. Hungar. 133 (1-2), 14–32, 2011
  24. K. Kuratow