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I-Sequentially Connectedness

Year 2024, Volume: 2 Issue: 1, 24 - 29, 31.05.2024

Abstract

This study, first, focuses on understanding two important ideas in ideal topological spaces: I-sequential openness and I-sequential closedness. We start by explaining what these sets are like and how they behave. Then, we talk about their interiors and closures. After that, we look at how these sets relate to the idea of connectedness, which is a key concept in topology. We call this connection I-sequentially connectedness. This helps us understand how sets are connected in ideal topological spaces.

References

  • O. Mucuk, Topoloji ve Kategori. Nobel Yayınları. Ankara, 2010.
  • R. Brown, Topology and Groupoids. Deganwy. United Kingdom, 2006.
  • N. Levine, “Semi-Open Sets and Semi Continuity in Topological Spaces,” Amer. Math. Monthly, vol. 70, no. 1, pp. 36–41, 1963, doi: 10.1080/00029890.1963.11990039.
  • O. Njastad, “On Some Classes of Nearly Open Sets,” Pacific J. Math., vol.15, no. 3, pp. 961–970, 1965.
  • A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, “On Pre-Continuous and Weak Pre-Continuous Mappings,” Proc. Math. Phys. Soc. Egypt, vol. 53, pp. 47–53, 1982.
  • M. E. Abd El-Monsef, E. F. Lashien, and A. A. Nasef, “On I-Open Sets and I-Continuous Function,” Kyungpook Math. J., vol. 32, no.1, pp. 21–30, Jun.1992.
  • K. Kuratowski, Topology, Volume I. Academic Press, New York, 1966.
  • E. Hayashi, “Topologies Defined by Local Properties,” Math. Ann., vol. 156, pp. 205–215, Jun. 1964, doi:/10.1007/BF01363287.
  • İ. Bukhatwa and S. Demiralp, “On Some Generalised Open Sets in Ideal Bitopological Spaces,” J. New Theory, vol. 32, pp. 1–10, Sep. 2020.
  • S. Kılınç, “I-Connectedness,” J. New Theory, vol. 39, pp. 1–7, Jun. 2022, doi:10.53570/jnt.1104540.
  • M. İlkhan, M. Akyiğit, and E. E. Kara, “On New Types of Sets via γ-Open Sets in Bitopological Spaces,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67 no.1, pp. 225–234, Feb. 2018, doi: 10.1501/Commua1_0000000844.
  • H. Z. Ibrahim and A. Mizyed, “On Semi-γ-I-Open Sets and a New Mapping,” IJMSC., vol. 6, no. 1, pp. 1–9, 2016.
  • A. Keskin, T. Noiri, and S. Yüksel, “Decompositions of I-Continuity and Continuity,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 53, no.2, pp. 67–75, 2004.
  • M. A. Al Shumrani, C. Özel, and A. Keskin Kaymakçı, “On Strong β-I-Open Sets and Decompositions of Continuity in Ideal Topological Spaces,” J. Math. Anal., vol. 8, no. 1, pp. 143–155, 2017.
  • O. Mucuk and T. Şahan, “On G-Sequential Continuity,” Filomat, vol. 28, pp. 1181–1189, 2014, doi: 10.2298/FIL1406181M.
  • H. F. Akız and L. Koçak, “Sequentially Hausdorff and Full Sequentially Hausdorff Spaces,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1724–1732, 2019, doi: 10.31801/cfsuasmas.424418.
  • C. Granados, “A New Notion of Convergence on Ideal Topological Spaces,” Sellecciones Matematicas, vol. 7, no. 2, pp. 250–256, 2020, doi: 10.17268/sel.mat.2020.02.07.
  • P. Kostyrko, T. Śalát, and T. W. Wilczýnski, “I-Convergence,” Real Anal. Exchange, vol. 26, no. 2, pp. 669–686, 2000/2001.
  • S. K. Pal, “I-Sequential Topological Spaces,” Appl. Math. E-Notes, vol.14, pp. 236–241, 2014.
  • E. Hatir and T. Noiri, “On Decompositions of Continuity via Idealization,” Acta Math. Hungar., vol. 96, pp. 341–349, Sep. 2002, doi: 10.1023/A:1019760901169.
  • S. Yüksel, Z. Güzel Ergül, and T. H. Şimşekler, “On Weakly θ-Pre-I Continuous Functions,” Sci. Stud. Res. Ser. Math. Inform., vol. 21, no. 2, pp. 157–172, 2011.
Year 2024, Volume: 2 Issue: 1, 24 - 29, 31.05.2024

Abstract

References

  • O. Mucuk, Topoloji ve Kategori. Nobel Yayınları. Ankara, 2010.
  • R. Brown, Topology and Groupoids. Deganwy. United Kingdom, 2006.
  • N. Levine, “Semi-Open Sets and Semi Continuity in Topological Spaces,” Amer. Math. Monthly, vol. 70, no. 1, pp. 36–41, 1963, doi: 10.1080/00029890.1963.11990039.
  • O. Njastad, “On Some Classes of Nearly Open Sets,” Pacific J. Math., vol.15, no. 3, pp. 961–970, 1965.
  • A. S. Mashhour, M. E. Abd El-Monsef, and S. N. El-Deeb, “On Pre-Continuous and Weak Pre-Continuous Mappings,” Proc. Math. Phys. Soc. Egypt, vol. 53, pp. 47–53, 1982.
  • M. E. Abd El-Monsef, E. F. Lashien, and A. A. Nasef, “On I-Open Sets and I-Continuous Function,” Kyungpook Math. J., vol. 32, no.1, pp. 21–30, Jun.1992.
  • K. Kuratowski, Topology, Volume I. Academic Press, New York, 1966.
  • E. Hayashi, “Topologies Defined by Local Properties,” Math. Ann., vol. 156, pp. 205–215, Jun. 1964, doi:/10.1007/BF01363287.
  • İ. Bukhatwa and S. Demiralp, “On Some Generalised Open Sets in Ideal Bitopological Spaces,” J. New Theory, vol. 32, pp. 1–10, Sep. 2020.
  • S. Kılınç, “I-Connectedness,” J. New Theory, vol. 39, pp. 1–7, Jun. 2022, doi:10.53570/jnt.1104540.
  • M. İlkhan, M. Akyiğit, and E. E. Kara, “On New Types of Sets via γ-Open Sets in Bitopological Spaces,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67 no.1, pp. 225–234, Feb. 2018, doi: 10.1501/Commua1_0000000844.
  • H. Z. Ibrahim and A. Mizyed, “On Semi-γ-I-Open Sets and a New Mapping,” IJMSC., vol. 6, no. 1, pp. 1–9, 2016.
  • A. Keskin, T. Noiri, and S. Yüksel, “Decompositions of I-Continuity and Continuity,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 53, no.2, pp. 67–75, 2004.
  • M. A. Al Shumrani, C. Özel, and A. Keskin Kaymakçı, “On Strong β-I-Open Sets and Decompositions of Continuity in Ideal Topological Spaces,” J. Math. Anal., vol. 8, no. 1, pp. 143–155, 2017.
  • O. Mucuk and T. Şahan, “On G-Sequential Continuity,” Filomat, vol. 28, pp. 1181–1189, 2014, doi: 10.2298/FIL1406181M.
  • H. F. Akız and L. Koçak, “Sequentially Hausdorff and Full Sequentially Hausdorff Spaces,” Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 2, pp. 1724–1732, 2019, doi: 10.31801/cfsuasmas.424418.
  • C. Granados, “A New Notion of Convergence on Ideal Topological Spaces,” Sellecciones Matematicas, vol. 7, no. 2, pp. 250–256, 2020, doi: 10.17268/sel.mat.2020.02.07.
  • P. Kostyrko, T. Śalát, and T. W. Wilczýnski, “I-Convergence,” Real Anal. Exchange, vol. 26, no. 2, pp. 669–686, 2000/2001.
  • S. K. Pal, “I-Sequential Topological Spaces,” Appl. Math. E-Notes, vol.14, pp. 236–241, 2014.
  • E. Hatir and T. Noiri, “On Decompositions of Continuity via Idealization,” Acta Math. Hungar., vol. 96, pp. 341–349, Sep. 2002, doi: 10.1023/A:1019760901169.
  • S. Yüksel, Z. Güzel Ergül, and T. H. Şimşekler, “On Weakly θ-Pre-I Continuous Functions,” Sci. Stud. Res. Ser. Math. Inform., vol. 21, no. 2, pp. 157–172, 2011.
There are 21 citations in total.

Details

Primary Language English
Subjects Topology
Journal Section Research Articles
Authors

Hürmet Fulya Akız 0000-0002-8547-2175

Kadriye Başar 0000-0003-2126-8199

Publication Date May 31, 2024
Submission Date March 26, 2024
Acceptance Date May 30, 2024
Published in Issue Year 2024 Volume: 2 Issue: 1

Cite

IEEE H. F. Akız and K. Başar, “I-Sequentially Connectedness”, BJS, vol. 2, no. 1, pp. 24–29, 2024.