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Homeomorphic Image of Some Kernels

Yıl 2020, Cilt: 17 Sayı: 1, 52 - 62, 01.05.2020

Öz

Through this paper, we shall study of kernels of a set with the help of ideals and boundaries of these kernels. We also study the convergence of the associated filter in terms of a point which comes from the kernels. We shall also study the homeomorphic images of these kernels.

Destekleyen Kurum

University Grants Commission (UGC), New Delhi-110002, India for granting UGC-NET Junior Research Fellowship )

Proje Numarası

(1173/(CSIR-UGC NET DEC. 2017)

Teşekkür

The second author is thankful to University Grants Commission (UGC), New Delhi-110002, India for granting UGC-NET Junior Research Fellowship (1173/(CSIR-UGC NET DEC. 2017)) during the tenure of which this work was done.

Kaynakça

  • [1] K. Kuratowski, Topology, Vol. I, New York, Academic Press, (1966).
  • [2] R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Co., New York, (1960).
  • [3] T. Natkaniec, On -continuity and -semicontinuity points, Mathematica Slovaca., 36(3), (1986), 297-312.
  • [4] A. Al-Omari, H. Al-Saadi, A topology via -local functions in ideal spaces, Mathematica, 60(83), (2018), 103-110.
  • [5] C. Bandhopadhya, S. Modak, A new topology via -operator, Proceedings of the National Academy of Sciences India, 76(A)IV, (2006), 317-320.
  • [6] T. R. Hamlett, D. Janković, Ideals in topological spaces and the set operator , Bollettino dell’Unione Matematica Italiana, 7 (4-B), (1990), 863-874.
  • [7] H. Hashimoto, On the -topology and its applications, Fundamenta Mathematicae, 91, (1976), 5-10.
  • [8] E. Hayashi, Topologies defined by local properties, Mathematische Annalen, 156, (1964), 205-215.
  • [9] D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly, 97,(1990), 295-310.
  • [10] S. Modak, Some new topologies on ideal topological spaces, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 82(3), (2012), 233-243.
  • [11] S. Modak, C. Bandyopadhyay, A note on -operator, Bulletin of the Malaysian Mathematical Sciences Society, 30(1), (2007), 43-48.
  • [12] P. Samuel, A topology formed from a given topology and ideal, London Mathematical Society, 10,(1975), 409-416.
  • [13] Sk. Selim, T. Noiri, S. Modak, Ideals and the associated filters on topological spaces, Eurasian Bulletin of Mathematics, 2(3), (2019), 80-85.
  • [14] N. Bourbaki, General Topology, Chapter 1-4, Springer, 1989.
  • [15] K. D. Joshi, Introduction to General Topology, Wiley, (1983).
  • [16] H. Maki, Generalized -sets and associated closure operator, The special Issue in Commemoration of Prof. Kazusada Ikeda's Retirement, (1986), 139-146.
  • [17] M. Caldas, S. Jafari, On some applications of b-open sets in topological spaces, Kochi Journal of Mathematics, 2, (2007), 11-19.
  • [18] D.Andrijević, Semi-preopen sets, Matematički Vesnik, 38, (1986), 24-32.
  • [19] D. Andrijević, On b-open sets, Matematički Vesnik, 48, (1996), 59-64.
  • [20] M. H. Stone, Applications of the theory of Boolean ring to general topology, Transactions of the American Mathematical Society, 41(3), (1937), 375-481.
Yıl 2020, Cilt: 17 Sayı: 1, 52 - 62, 01.05.2020

Öz

Proje Numarası

(1173/(CSIR-UGC NET DEC. 2017)

Kaynakça

  • [1] K. Kuratowski, Topology, Vol. I, New York, Academic Press, (1966).
  • [2] R. Vaidyanathaswamy, Set Topology, Chelsea Publishing Co., New York, (1960).
  • [3] T. Natkaniec, On -continuity and -semicontinuity points, Mathematica Slovaca., 36(3), (1986), 297-312.
  • [4] A. Al-Omari, H. Al-Saadi, A topology via -local functions in ideal spaces, Mathematica, 60(83), (2018), 103-110.
  • [5] C. Bandhopadhya, S. Modak, A new topology via -operator, Proceedings of the National Academy of Sciences India, 76(A)IV, (2006), 317-320.
  • [6] T. R. Hamlett, D. Janković, Ideals in topological spaces and the set operator , Bollettino dell’Unione Matematica Italiana, 7 (4-B), (1990), 863-874.
  • [7] H. Hashimoto, On the -topology and its applications, Fundamenta Mathematicae, 91, (1976), 5-10.
  • [8] E. Hayashi, Topologies defined by local properties, Mathematische Annalen, 156, (1964), 205-215.
  • [9] D. Janković, T. R. Hamlett, New topologies from old via ideals, The American Mathematical Monthly, 97,(1990), 295-310.
  • [10] S. Modak, Some new topologies on ideal topological spaces, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, 82(3), (2012), 233-243.
  • [11] S. Modak, C. Bandyopadhyay, A note on -operator, Bulletin of the Malaysian Mathematical Sciences Society, 30(1), (2007), 43-48.
  • [12] P. Samuel, A topology formed from a given topology and ideal, London Mathematical Society, 10,(1975), 409-416.
  • [13] Sk. Selim, T. Noiri, S. Modak, Ideals and the associated filters on topological spaces, Eurasian Bulletin of Mathematics, 2(3), (2019), 80-85.
  • [14] N. Bourbaki, General Topology, Chapter 1-4, Springer, 1989.
  • [15] K. D. Joshi, Introduction to General Topology, Wiley, (1983).
  • [16] H. Maki, Generalized -sets and associated closure operator, The special Issue in Commemoration of Prof. Kazusada Ikeda's Retirement, (1986), 139-146.
  • [17] M. Caldas, S. Jafari, On some applications of b-open sets in topological spaces, Kochi Journal of Mathematics, 2, (2007), 11-19.
  • [18] D.Andrijević, Semi-preopen sets, Matematički Vesnik, 38, (1986), 24-32.
  • [19] D. Andrijević, On b-open sets, Matematički Vesnik, 48, (1996), 59-64.
  • [20] M. H. Stone, Applications of the theory of Boolean ring to general topology, Transactions of the American Mathematical Society, 41(3), (1937), 375-481.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Shyamapada Modak

Jiarul Haque Bu kişi benim 0000-0003-1055-9820

Sk Selim Bu kişi benim 0000-0002-4226-2004

Proje Numarası (1173/(CSIR-UGC NET DEC. 2017)
Yayımlanma Tarihi 1 Mayıs 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 17 Sayı: 1

Kaynak Göster

APA Modak, S., Haque, J., & Selim, S. (2020). Homeomorphic Image of Some Kernels. Cankaya University Journal of Science and Engineering, 17(1), 52-62.
AMA Modak S, Haque J, Selim S. Homeomorphic Image of Some Kernels. CUJSE. Mayıs 2020;17(1):52-62.
Chicago Modak, Shyamapada, Jiarul Haque, ve Sk Selim. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering 17, sy. 1 (Mayıs 2020): 52-62.
EndNote Modak S, Haque J, Selim S (01 Mayıs 2020) Homeomorphic Image of Some Kernels. Cankaya University Journal of Science and Engineering 17 1 52–62.
IEEE S. Modak, J. Haque, ve S. Selim, “Homeomorphic Image of Some Kernels”, CUJSE, c. 17, sy. 1, ss. 52–62, 2020.
ISNAD Modak, Shyamapada vd. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering 17/1 (Mayıs 2020), 52-62.
JAMA Modak S, Haque J, Selim S. Homeomorphic Image of Some Kernels. CUJSE. 2020;17:52–62.
MLA Modak, Shyamapada vd. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering, c. 17, sy. 1, 2020, ss. 52-62.
Vancouver Modak S, Haque J, Selim S. Homeomorphic Image of Some Kernels. CUJSE. 2020;17(1):52-6.