KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 46 Issue: 4

Decompositions of continuity for multifunctions

Marian Przemski
Sayfa
—
Yayın Tarihi
2017-08-01
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 this purpose we will generalize the methods introduced by the author in [27] and later used in [9] and in many papers including for example [10] and [23].

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Investigations of decompositions of continuity for functions between topological spaces has a large literature, but extension of this topic to multifunctions has not yet been investigated.
📊
Temel Bulgular & Veri:The aim of the present note is to introduce the study of decompositions of continuity for multifunctions.
💡
Sonuç & Katkı:For this purpose we will generalize the methods introduced by the author in [27] and later used in [9] and in many papers including for example [10] and [23].
🔬Tür:Research Article
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:D(c · $\alpha$)- · D(c

Abstract

Investigations of decompositions of continuity for functions between topological spaces has a large literature, but extension of this topic to multifunctions has not yet been investigated. The aim of the present note is to introduce the study of decompositions of continuity for multifunctions. For this purpose we will generalize the methods introduced by the author in [27] and later used in [9] and in many papers including for example [10] and [23].

🔖

Bu Makaleye Atıf Yap

Przemski, M. (2017). Decompositions of continuity for multifunctions. Hacettepe Journal of Mathematics and Statistics, Volume: 46 Issue: 4. https://ajindex.com/articles/1403019

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (37)

  1. D. Andrijevic, Semi-preopen sets, Mat Vesnik. 38(1986), 24-32.
  2. D. Andrijevic, On b-open sets, Mat Bech. 48(1996),59-64.
  3. A.A. El-Atik, A study of some types of mappings on topological spaces, Master's Thesis. Faculty of Science, Tanta University, (1997).
  4. C. Berge, Espaces topologiques fonctions multivaques, Dunod, Paris, (1959).
  5. C. Choquet, Lectures on Analysis, Benjamin, Vol. I, New York, Amsterdam (1969).
  6. J.P.R. Christensen, Theorems of J. Namioka and R.E.Johnson type for upper semi- continuous and compact-valued set-valued maps, Proc. Amer. Math. Soc. 86(1982), 649-655.
  7. M.M. Coban, P.S. Kenderov, J.P. Revalski, Densely dened selections of multivalued map- pings, Trans. Amer. Math. Soc. 344(1994), 533-552.
  8. S.G. Crossley, S.K. Hildebrand Semi-closure, Texas J. Sci. 22(1971), 99-112.
  9. J. Dontchev, M. Przemski, On the various decompositions of continuous and some weakly continuous functions, Acta Math. Hungar. 71(1996),109-120.
  10. E. Hatir, M. Caldas, On decompositions of continuity and $\alpha$-continuity, Arabian Journal for Science and Engineering 35(2010),197-202.
  11. S. Kempisty, Sur les functions quasicontinues, Fund. Math., 19(1932), 184-197.
  12. M. Lassonde, J. Revalski, Fragmentability of sequences of set-valued mappings with applications to variational principles, Proc. Amer. Math. Soc. 133(2005), 2637-46.
  13. K. Kuratowski, Topology, I, New York (1966).
  14. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.
  15. A.S. Mashhour, I.A. Hasanein, S.N. El-Deeb, $\alpha$-continuous and $\alpha$-open mappings, Acta Math. Hungar., 41(1983), 213-218.
  16. A.S. Mashhour, M.E. El-Monsef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Phys. Soc. Egypt 53(1982), 47-53.
  17. M.E. El-Monsef, S.N. El-Deeb, R.A. Mahmoud, $\beta$-Open sets and $\beta$-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12(1983), 77-90.
  18. M.E. El-Monsef, M.E. Abd El-Monsef, A.A. Nasef, On multifunctions, Chaos, Solutions and Fractals, 12(2001), 2387-94.
  19. W.B. Moors, J.R. Gilas, Generic continuity of minimal set-valued mappings, J. Austral. Math.Soc. Ser. A 63(1997), 238-62.
  20. T. Neubrunn, Strongly quasi-continuous multivalued mappings, Gen. Top. and its Rel. Mod. Anal. Algebra VI(1988), 351-59.
  21. O. Njastad, On some classes of nearly open sets, Pacic J. Math. 15(1965), 961-70.
  22. V.I. Ponomarev, Properties of topological spaces preserved under multivalued continuous mappings on compacta, Amer. Math. Soc. Trans. 38(2)(1964), 119-140.
  23. T. Noiri, V. Popa, On decompositions of continuity in topological spaces, Acta Mathematica Hungarica 128 (2010),175-189.
  24. V. Popa, Some properties of H-almost continuous multifunctions, Problemy Mat. 10(1990), 9-26.
  25. V. Popa, On a decomposition of quasicontinuity for multifunctions, Stud. Cerc. Mat. 27(1975), 323-328.
  26. V. Popa, T. Noiri, On upper and lower $\beta$-continuous multifunctions, Real Analysis Exchange 22(1996/97), 362367.
  27. M. Przemski, A decomposition of continuity and $\alpha$-continuity, Acta Math. Hungar. 61(1993), 93-98.
  28. M. Przemski, On the relationships between the graphs of multifunctions, Demonstratio Math. 41(2008), 203-224.
  29. E. Hatir, M. Caldas, On decompositions of continuity and $\alpha$-continuity, Arabian Journal for Science and Engineering 35(2010),197-202.
  30. N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41.
  31. A.S. Mashhour, M.E. El-Monsef, S.N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Phys. Soc. Egypt 53(1982), 47-53.
  32. M.E. El-Monsef, S.N. El-Deeb, R.A. Mahmoud, $\beta$-Open sets and $\beta$-continuous mappings, Bull. Fac. Sci. Assiut Univ. 12(1983), 77-90.
  33. M.E. El-Monsef, M.E. Abd El-Monsef, A.A. Nasef, On multifunctions, Chaos, Solutions and Fractals, 12(2001), 2387-94.
  34. O. Njastad, On some classes of nearly open sets, Pacic J. Math. 15(1965), 961-70.
  35. V.I. Ponomarev, Properties of topological spaces preserved under multivalued continuous mappings on compacta, Amer. Math. Soc. Trans. 38(2)(1964), 119-140.
  36. V. Popa, On a decomposition of quasicontinuity for multifunctions, Stud. Cerc. Mat. 27(1975), 323-328.
  37. M. Przemski, A decomposition of continuity and $\alpha$-continuity, Acta Math. Hungar. 61(1993), 93-98.