Research Article
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Year 2023, Volume: 52 Issue: 1, 163 - 170, 15.02.2023
https://doi.org/10.15672/hujms.1101438

Abstract

References

  • [1] A. Di Concilio, C. Guadagni, J. F. Peters and S. Ramanna, Descriptive Proximities: Properties and interplay between classical proximities and overlap, Mathematics in Computer Science 12 (1), 91-106, 2018.
  • [2] V. A. Efremovič, Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian) 76, 341-343, 1951.
  • [3] V. A. Efremovič, The geometry of proximity I, Mat. Sb. (N. S.) (Russian) 31 (73), 189-200, 1952.
  • [4] T. Husein, Introduction to Topological Groups, W.B. Sauders Company, 1966.
  • [5] E. İnan, Approximately semigroups and ideals: An algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering 17, 479-487, 2017.
  • [6] E. İnan, Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science 8 (1), 24-41, 2018.
  • [7] E. İnan, Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1), 572-582, 2019.
  • [8] E. İnan, Approximately rings in proximal relator spaces, Turkish J. Math. 43, 2941- 2953, 2019.
  • [9] E. İnan and M. Uçkun, Approximately $\Gamma$-semigroups in proximal relator spaces, Appl. Algebra Eng. Commun. Comput. 30 (4), 299-311, 2019.
  • [10] M. Kovăr, A new causal topology and why the universe is co-compact, arXiv: 1112.0817 [math-ph], 1-15, 2011.
  • [11] S. A. Naimpally and J. F. Peters, Topology with Applications: Topological Spaces via Near and Far, World Scientific, 2013.
  • [12] S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge University Press, 1970.
  • [13] J. F. Peters and S. A. Naimpally, Applications of near sets, Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
  • [14] M. Uçkun, Approximately $\Gamma$-rings in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2), 1780-1796, 2019.

Semitopological $\delta$-groups

Year 2023, Volume: 52 Issue: 1, 163 - 170, 15.02.2023
https://doi.org/10.15672/hujms.1101438

Abstract

The aim of this paper is to introduce semitopological $\delta$-group and topological $\delta$-group with the concept of $\delta$-group which arise from approximately algebraic structures. Furthermore, it is shown that product space determined with $\delta$-topological subspaces is a $\delta$-topological space. Fundamental system of open $\delta$-neighborhoods and related properties were investigated.

References

  • [1] A. Di Concilio, C. Guadagni, J. F. Peters and S. Ramanna, Descriptive Proximities: Properties and interplay between classical proximities and overlap, Mathematics in Computer Science 12 (1), 91-106, 2018.
  • [2] V. A. Efremovič, Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian) 76, 341-343, 1951.
  • [3] V. A. Efremovič, The geometry of proximity I, Mat. Sb. (N. S.) (Russian) 31 (73), 189-200, 1952.
  • [4] T. Husein, Introduction to Topological Groups, W.B. Sauders Company, 1966.
  • [5] E. İnan, Approximately semigroups and ideals: An algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering 17, 479-487, 2017.
  • [6] E. İnan, Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science 8 (1), 24-41, 2018.
  • [7] E. İnan, Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1), 572-582, 2019.
  • [8] E. İnan, Approximately rings in proximal relator spaces, Turkish J. Math. 43, 2941- 2953, 2019.
  • [9] E. İnan and M. Uçkun, Approximately $\Gamma$-semigroups in proximal relator spaces, Appl. Algebra Eng. Commun. Comput. 30 (4), 299-311, 2019.
  • [10] M. Kovăr, A new causal topology and why the universe is co-compact, arXiv: 1112.0817 [math-ph], 1-15, 2011.
  • [11] S. A. Naimpally and J. F. Peters, Topology with Applications: Topological Spaces via Near and Far, World Scientific, 2013.
  • [12] S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge University Press, 1970.
  • [13] J. F. Peters and S. A. Naimpally, Applications of near sets, Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
  • [14] M. Uçkun, Approximately $\Gamma$-rings in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2), 1780-1796, 2019.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Ebubekir İnan 0000-0002-7269-8941

Mustafa Uçkun 0000-0003-1813-5272

Publication Date February 15, 2023
Published in Issue Year 2023 Volume: 52 Issue: 1

Cite

APA İnan, E., & Uçkun, M. (2023). Semitopological $\delta$-groups. Hacettepe Journal of Mathematics and Statistics, 52(1), 163-170. https://doi.org/10.15672/hujms.1101438
AMA İnan E, Uçkun M. Semitopological $\delta$-groups. Hacettepe Journal of Mathematics and Statistics. February 2023;52(1):163-170. doi:10.15672/hujms.1101438
Chicago İnan, Ebubekir, and Mustafa Uçkun. “Semitopological $\delta$-Groups”. Hacettepe Journal of Mathematics and Statistics 52, no. 1 (February 2023): 163-70. https://doi.org/10.15672/hujms.1101438.
EndNote İnan E, Uçkun M (February 1, 2023) Semitopological $\delta$-groups. Hacettepe Journal of Mathematics and Statistics 52 1 163–170.
IEEE E. İnan and M. Uçkun, “Semitopological $\delta$-groups”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, pp. 163–170, 2023, doi: 10.15672/hujms.1101438.
ISNAD İnan, Ebubekir - Uçkun, Mustafa. “Semitopological $\delta$-Groups”. Hacettepe Journal of Mathematics and Statistics 52/1 (February 2023), 163-170. https://doi.org/10.15672/hujms.1101438.
JAMA İnan E, Uçkun M. Semitopological $\delta$-groups. Hacettepe Journal of Mathematics and Statistics. 2023;52:163–170.
MLA İnan, Ebubekir and Mustafa Uçkun. “Semitopological $\delta$-Groups”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 1, 2023, pp. 163-70, doi:10.15672/hujms.1101438.
Vancouver İnan E, Uçkun M. Semitopological $\delta$-groups. Hacettepe Journal of Mathematics and Statistics. 2023;52(1):163-70.