Year 2020, Volume 17 , Issue 1, Pages 52 - 62 2020-05-01

Homeomorphic Image of Some Kernels

Shyamapada MODAK [1] , Jiarul HAQUE [2] , Sk SELİM [3]


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.
filter, associated filter, , fontier points, local function, homeomorphism
  • [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.
Primary Language en
Subjects Engineering
Published Date Bahar
Journal Section Articles
Authors

Author: Shyamapada MODAK (Primary Author)
Institution: University of Gour Banga
Country: India


Orcid: 0000-0003-1055-9820
Author: Jiarul HAQUE
Institution: University of Gour Banga
Country: India


Orcid: 0000-0002-4226-2004
Author: Sk SELİM
Institution: University of Gour Banga
Country: India


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.
Dates

Publication Date : May 1, 2020

Bibtex @research article { cankujse705355, journal = {Cankaya University Journal of Science and Engineering}, issn = {1309-6788}, eissn = {2564-7954}, address = {}, publisher = {Cankaya University}, year = {2020}, volume = {17}, pages = {52 - 62}, doi = {}, title = {Homeomorphic Image of Some Kernels}, key = {cite}, author = {Modak, Shyamapada and Haque, Jiarul and Seli̇m, Sk} }
APA Modak, S , Haque, J , Seli̇m, S . (2020). Homeomorphic Image of Some Kernels . Cankaya University Journal of Science and Engineering , 17 (1) , 52-62 . Retrieved from https://dergipark.org.tr/en/pub/cankujse/issue/54098/705355
MLA Modak, S , Haque, J , Seli̇m, S . "Homeomorphic Image of Some Kernels" . Cankaya University Journal of Science and Engineering 17 (2020 ): 52-62 <https://dergipark.org.tr/en/pub/cankujse/issue/54098/705355>
Chicago Modak, S , Haque, J , Seli̇m, S . "Homeomorphic Image of Some Kernels". Cankaya University Journal of Science and Engineering 17 (2020 ): 52-62
RIS TY - JOUR T1 - Homeomorphic Image of Some Kernels AU - Shyamapada Modak , Jiarul Haque , Sk Seli̇m Y1 - 2020 PY - 2020 N1 - DO - T2 - Cankaya University Journal of Science and Engineering JF - Journal JO - JOR SP - 52 EP - 62 VL - 17 IS - 1 SN - 1309-6788-2564-7954 M3 - UR - Y2 - 2020 ER -
EndNote %0 Çankaya Üniversitesi Bilim ve Mühendislik Dergisi Homeomorphic Image of Some Kernels %A Shyamapada Modak , Jiarul Haque , Sk Seli̇m %T Homeomorphic Image of Some Kernels %D 2020 %J Cankaya University Journal of Science and Engineering %P 1309-6788-2564-7954 %V 17 %N 1 %R %U
ISNAD Modak, Shyamapada , Haque, Jiarul , Seli̇m, Sk . "Homeomorphic Image of Some Kernels". Cankaya University Journal of Science and Engineering 17 / 1 (May 2020): 52-62 .
AMA Modak S , Haque J , Seli̇m S . Homeomorphic Image of Some Kernels. Cankaya University Journal of Science and Engineering. 2020; 17(1): 52-62.
Vancouver Modak S , Haque J , Seli̇m S . Homeomorphic Image of Some Kernels. Cankaya University Journal of Science and Engineering. 2020; 17(1): 52-62.