KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 5

Quantale-valued uniform convergence towers for quantale-valued metric spaces

Gunther Jäger0000-0002-1495-4564
Sayfa
—
Yayın Tarihi
2019-10-08
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:We show that quantale-valued metric spaces and quantale-valued partial metric spaces allow natural quantale-valued uniform convergence structures.
📊
Temel Bulgular & Veri:We furthermore characterize quantale-valued metric spaces and quantale-valued partial metric spaces by these quantale-valued uniform convergence structures.
💡
Sonuç & Katkı:For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$L$-metric space · $L$-partial metric space · $L$-uniform convergence tower space

Abstract

We show that quantale-valued metric spaces and quantale-valued partial metric spaces allow natural quantale-valued uniform convergence structures. We furthermore characterize quantale-valued metric spaces and quantale-valued partial metric spaces by these quantale-valued uniform convergence structures. For special choices of the quantale, the results specialize to metric spaces and probabilistic metric spaces.

🔖

Bu Makaleye Atıf Yap

Jäger, G. (2019). Quantale-valued uniform convergence towers for quantale-valued metric spaces. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 5. https://ajindex.com/articles/1402743

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (22)

  1. J. Adámek, H. Herrlich, and G.E. Strecker, Abstract and Concrete Categories, Wiley, New York, 1989.
  2. T.M.G. Ahsanullah and G. Jäger, Probabilistic uniform convergence spaces redefined, Acta Math. Hungarica, 146, 376–390, 2015.
  3. N. Bourbaki, General topology, Chapters 1 – 4, Springer Verlag, Berlin - Heidelberg - New York - London - Paris - Tokyo, 1990.
  4. P. Brock, Probabilistic convergence spaces and generalized metric spaces, Int. J. Math. and Math. Sci. 21, 439–452, 1998.
  5. P. Brock and D.C. Kent, Approach spaces, limit tower spaces, and probabilistic con- vergence spaces, Appl. Cat. Structures, 5, 99–110, 1997.
  6. R.C. Flagg, Completeness in continuity spaces, in: Category Theory 1991, CMS Conf. Proc. 13, 183–199, 1992.
  7. R.C. Flagg, Quantales and continuity spaces, Algebra Univers. 37, 257–276, 1997.
  8. L.C. Florescu, Probabilistic convergence structures, Aequationes Math. 38, 123–145, 1989.
  9. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove and D.S. Scott, Continuous lattices and domains, Cambridge University Press, 2003.
  10. G. Jäger, A convergence theory for probabilistic metric spaces, Quaest. Math. 38, 587–599, 2015.
  11. G. Jäger, A common framework for lattice-valued, probabilistic and approach uniform (convergence) spaces, Iran. J. Fuzzy Syst. 14, 67–82, 2017.
  12. G. Jäger and T.M.G. Ahsanullah, Characterization of quantale-valued metric spaces and quantale-valued partial metric spaces by convergence, Appl. Gen. Topol. 19 (1), 129–144, 2018.
  13. R. Kopperman, S. Matthews and H. Pajoohesh, Partial metrizability in value quan- tales, Appl. Gen. Topol. 5, 115 – 127, 2004.
  14. F.W. Lawvere, Metric spaces, generalized logic, and closed categories, Rendiconti del Seminario Matematico e Fisico di Milano, 43, 135–166, 1973. Reprinted in: Repr. Theory Appl. Categ. 1, 1–37, 2002.
  15. Y.J. Lee and B. Windels, Transitivity in uniform approach theory, Int. J. Math. Math. Sci. 32, 707–720, 2002.
  16. R. Lowen, Approach spaces. The missing link in the topology-uniformity-metric triad, Claredon Press, Oxford, 1997.
  17. H. Nusser, A generalization of probabilistic uniform spaces, Appl. Categ. Structures, 10, 81–98, 2002.
  18. G. Preuss, Foundations of topology. An approach to convenient topology, Kluwer Aca- demic Publishers, Dordrecht, 2002.
  19. G.N. Raney, A subdirect-union representation for completely distributive complete lattices, Proc. Amer. Math. Soc. 4, 518–512, 1953.
  20. G.D. Richardson and D.C. Kent, Probabilistic convergence spaces, J. Austral. Math. Soc. (Series A), 61, 400–420, 1996.
  21. B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, New York, 1983.
  22. R.M. Tardiff, Topologies for probabilistic metric spaces, Pacific J. Math. 65, 233–251, 1976.