Research Article
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I-Connectedness

Year 2022, Issue: 39, 1 - 7, 30.06.2022
https://doi.org/10.53570/jnt.1104540
https://izlik.org/JA96UH73XU

Abstract

In this paper, we introduce a weak form of connectedness with respect to an ideal. We also investigate its relation to connectedness. We examine the I-connectedness property on the new topology introduced by the ideal. In addition, it is revealed under what conditions I-connectedness and connectedness coincide and one differs from another.

References

  • R. Vaidyanathaswamy, The Localisation Theory in Set Topology, Proceedings of the Indian Academy of Sciences 20 (1945) 51–61.
  • K. Kuratowski, Topology, Volume I, Academic Press, New York, 1966.
  • E. Ekici, T. Noiri, Connectedness in Ideal Topological Spaces, Novi Sad Journal of Mathematics 38 (2) (2008) 65–70.
  • N. Sathiyasundari, V. Renukadevi, Note on ∗-Connected Ideal Spaces, Novi Sad Journal of Mathematics 42 (1) (2012) 15–20.
  • S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat 29 (4) (2015) 661–665.
  • S. Kilinc, More on ∗∗-Connectedness, Matematichki Bilten 43 (2) (2019) 53–60.
  • B. K. Tyagi, M. Bhardwaj, S. Singh, Cl*-Connectedness and Cl-Cl*-Connectedness in Ideal Topological Spaces, Matematichki Bilten 42 (2) (2018) 91–100.
  • D. Jankovic, T. R. Hamlett, New Topologies from Old via Ideals, The American Mathematical Monthly 97(4) (1990) 295–310.
  • O. Njåstad, Remarks on Topologies Defined by Local Properties, Avhandlinger Norske Videnskaps-Akademi Oslo, Universitetsforlaget, 1966.
  • R. L. Newcomb, Topologies Which are Compact Modulo an Ideal, PhD Dissertation, University of California (1967) Santa Barbara, USA.
  • E. Ekici, T. Noiri, ∗-Hyperconnected Ideal Topological Spaces, Analele Stiintifice ale Universitatii Al I Cuza din lasi-Matematica, Tomul 58 (1) (2012) 121–129.
  • A. Keskin, S., Yüksel, T. Noiri, On I-Extremally Disconnected Spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56 (1) (2007) 33–40.

Year 2022, Issue: 39, 1 - 7, 30.06.2022
https://doi.org/10.53570/jnt.1104540
https://izlik.org/JA96UH73XU

Abstract

References

  • R. Vaidyanathaswamy, The Localisation Theory in Set Topology, Proceedings of the Indian Academy of Sciences 20 (1945) 51–61.
  • K. Kuratowski, Topology, Volume I, Academic Press, New York, 1966.
  • E. Ekici, T. Noiri, Connectedness in Ideal Topological Spaces, Novi Sad Journal of Mathematics 38 (2) (2008) 65–70.
  • N. Sathiyasundari, V. Renukadevi, Note on ∗-Connected Ideal Spaces, Novi Sad Journal of Mathematics 42 (1) (2012) 15–20.
  • S. Modak, T. Noiri, Connectedness of Ideal Topological Spaces, Filomat 29 (4) (2015) 661–665.
  • S. Kilinc, More on ∗∗-Connectedness, Matematichki Bilten 43 (2) (2019) 53–60.
  • B. K. Tyagi, M. Bhardwaj, S. Singh, Cl*-Connectedness and Cl-Cl*-Connectedness in Ideal Topological Spaces, Matematichki Bilten 42 (2) (2018) 91–100.
  • D. Jankovic, T. R. Hamlett, New Topologies from Old via Ideals, The American Mathematical Monthly 97(4) (1990) 295–310.
  • O. Njåstad, Remarks on Topologies Defined by Local Properties, Avhandlinger Norske Videnskaps-Akademi Oslo, Universitetsforlaget, 1966.
  • R. L. Newcomb, Topologies Which are Compact Modulo an Ideal, PhD Dissertation, University of California (1967) Santa Barbara, USA.
  • E. Ekici, T. Noiri, ∗-Hyperconnected Ideal Topological Spaces, Analele Stiintifice ale Universitatii Al I Cuza din lasi-Matematica, Tomul 58 (1) (2012) 121–129.
  • A. Keskin, S., Yüksel, T. Noiri, On I-Extremally Disconnected Spaces, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 56 (1) (2007) 33–40.
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Selahattin Kılınç 0000-0003-3708-9443

Submission Date April 16, 2022
Publication Date June 30, 2022
DOI https://doi.org/10.53570/jnt.1104540
IZ https://izlik.org/JA96UH73XU
Published in Issue Year 2022 Issue: 39

Cite

APA Kılınç, S. (2022). I-Connectedness. Journal of New Theory, 39, 1-7. https://doi.org/10.53570/jnt.1104540
AMA 1.Kılınç S. I-Connectedness. JNT. 2022;(39):1-7. doi:10.53570/jnt.1104540
Chicago Kılınç, Selahattin. 2022. “I-Connectedness”. Journal of New Theory, nos. 39: 1-7. https://doi.org/10.53570/jnt.1104540.
EndNote Kılınç S (June 1, 2022) I-Connectedness. Journal of New Theory 39 1–7.
IEEE [1]S. Kılınç, “I-Connectedness”, JNT, no. 39, pp. 1–7, June 2022, doi: 10.53570/jnt.1104540.
ISNAD Kılınç, Selahattin. “I-Connectedness”. Journal of New Theory. 39 (June 1, 2022): 1-7. https://doi.org/10.53570/jnt.1104540.
JAMA 1.Kılınç S. I-Connectedness. JNT. 2022;:1–7.
MLA Kılınç, Selahattin. “I-Connectedness”. Journal of New Theory, no. 39, June 2022, pp. 1-7, doi:10.53570/jnt.1104540.
Vancouver 1.Selahattin Kılınç. I-Connectedness. JNT. 2022 Jun. 1;(39):1-7. doi:10.53570/jnt.1104540


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