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Homeomorphic Image of Some Kernels

Year 2020, Volume: 17 Issue: 1, 52 - 62, 01.05.2020

Abstract

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.

Supporting Institution

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

Project Number

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

Thanks

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.

References

  • [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.
Year 2020, Volume: 17 Issue: 1, 52 - 62, 01.05.2020

Abstract

Project Number

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

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Shyamapada Modak

Jiarul Haque This is me 0000-0003-1055-9820

Sk Selim This is me 0000-0002-4226-2004

Project Number (1173/(CSIR-UGC NET DEC. 2017)
Publication Date May 1, 2020
Published in Issue Year 2020 Volume: 17 Issue: 1

Cite

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. May 2020;17(1):52-62.
Chicago Modak, Shyamapada, Jiarul Haque, and Sk Selim. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering 17, no. 1 (May 2020): 52-62.
EndNote Modak S, Haque J, Selim S (May 1, 2020) Homeomorphic Image of Some Kernels. Cankaya University Journal of Science and Engineering 17 1 52–62.
IEEE S. Modak, J. Haque, and S. Selim, “Homeomorphic Image of Some Kernels”, CUJSE, vol. 17, no. 1, pp. 52–62, 2020.
ISNAD Modak, Shyamapada et al. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering 17/1 (May 2020), 52-62.
JAMA Modak S, Haque J, Selim S. Homeomorphic Image of Some Kernels. CUJSE. 2020;17:52–62.
MLA Modak, Shyamapada et al. “Homeomorphic Image of Some Kernels”. Cankaya University Journal of Science and Engineering, vol. 17, no. 1, 2020, pp. 52-62.
Vancouver Modak S, Haque J, Selim S. Homeomorphic Image of Some Kernels. CUJSE. 2020;17(1):52-6.