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Approximately Groups in Proximal Relator Spaces

Year 2019, Volume: 68 Issue: 1, 572 - 582, 01.02.2019
https://doi.org/10.31801/cfsuasmas.438380

Abstract

The focus of this article is on defining descriptive approximations of sets or algebraic structures in proximal relator spaces. By way of a practical application, descriptive approximately algebraic structures such as groupoids, semigroups and groups in digital images endowed with descriptive Efremovic proximity relations are introduced.

References

  • Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., 1961, xv+224pp.
  • Efremovic, V. A., Infinitesimal spaces (in Russian), Doklady Akad. Nauk SSSR (N.S.), 76 (1951), 341-343.
  • Efremovic, V. A., The geometry of proximity I (in Russian), Mat. Sb. (N.S.) 31 (73) (1952), no. 1, 189-200.
  • Henry, C. J. and Smith, G., Proximity system: A description-based system for quantifying the nearness or apartness of visual rough sets, Transactions on Rough Sets XVII. 8375 (2014), 48-73.
  • İnan, E. and Öztürk, M. A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat. 41 (2012), no. 4, 545-558.
  • İnan, E. and Öztürk, M. A., Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat. 43 (2014), no. 2, 279-281.
  • İnan, E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17 (2017) 479-487.
  • Kovár, M. M., A new causal topology and why the universe is co-compact, arXive:1112.0817[math-ph] (2011) 1-15 arXiv:1112.0817.
  • Lodato, M. W., On topologically induced generalized proximity relations, Ph.D. thesis, Rutgers University, 1962.
  • Lodato, M. W., On topologically induced generalized proximity relations I, Proc. Amer. Math. Soc. 15 (1964), 417-422.
  • Lodato, M. W., On topologically induced generalized proximity relations II, Pacific J. Math. 17 (1966), 131-135.
  • Naimpally, S. A. and Peters, J. F., Topology with Applications. Topological Spaces via Near and Far, World Scientific, Sinapore, 2013.
  • Öztürk, M. A., Uçkun, M. and İnan, E., Near group of weak cosets on nearness approximation spaces, Fund. Inform. 133 (2014), 433-448.
  • Peters, J. F., Proximal relator spaces, Filomat, 30 (2016), no. 2, 469-472, MR3593041.
  • Peters, J. F. and Naimpally, S. A., Applications of near sets, Notices of the Amer. Math. Soc. 59 (2012), no. 4, 536-542.
  • Peters, J. F., Near sets: An introduction, Math. in Comp. Sci. 7 (2013), no. 1, 3-9.
  • Peters, J. F., İnan, E. and Öztürk, M. A., Spatial and descriptive isometries in proximity spaces , General Mathematics Notes, 21 (2014), no. 2, 1-10.
  • Peters, J. F., Öztürk, M. A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science, 5 (1), 1-13, 2015.
  • Száz, A., Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50 (1987), no. 3-4, 177-201, MR0918156.
Year 2019, Volume: 68 Issue: 1, 572 - 582, 01.02.2019
https://doi.org/10.31801/cfsuasmas.438380

Abstract

References

  • Clifford, A. H. and Preston, G. B., The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., 1961, xv+224pp.
  • Efremovic, V. A., Infinitesimal spaces (in Russian), Doklady Akad. Nauk SSSR (N.S.), 76 (1951), 341-343.
  • Efremovic, V. A., The geometry of proximity I (in Russian), Mat. Sb. (N.S.) 31 (73) (1952), no. 1, 189-200.
  • Henry, C. J. and Smith, G., Proximity system: A description-based system for quantifying the nearness or apartness of visual rough sets, Transactions on Rough Sets XVII. 8375 (2014), 48-73.
  • İnan, E. and Öztürk, M. A., Near groups on nearness approximation spaces, Hacet. J. Math. Stat. 41 (2012), no. 4, 545-558.
  • İnan, E. and Öztürk, M. A., Erratum and notes for near groups on nearness approximation spaces, Hacet. J. Math. Stat. 43 (2014), no. 2, 279-281.
  • İnan, E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17 (2017) 479-487.
  • Kovár, M. M., A new causal topology and why the universe is co-compact, arXive:1112.0817[math-ph] (2011) 1-15 arXiv:1112.0817.
  • Lodato, M. W., On topologically induced generalized proximity relations, Ph.D. thesis, Rutgers University, 1962.
  • Lodato, M. W., On topologically induced generalized proximity relations I, Proc. Amer. Math. Soc. 15 (1964), 417-422.
  • Lodato, M. W., On topologically induced generalized proximity relations II, Pacific J. Math. 17 (1966), 131-135.
  • Naimpally, S. A. and Peters, J. F., Topology with Applications. Topological Spaces via Near and Far, World Scientific, Sinapore, 2013.
  • Öztürk, M. A., Uçkun, M. and İnan, E., Near group of weak cosets on nearness approximation spaces, Fund. Inform. 133 (2014), 433-448.
  • Peters, J. F., Proximal relator spaces, Filomat, 30 (2016), no. 2, 469-472, MR3593041.
  • Peters, J. F. and Naimpally, S. A., Applications of near sets, Notices of the Amer. Math. Soc. 59 (2012), no. 4, 536-542.
  • Peters, J. F., Near sets: An introduction, Math. in Comp. Sci. 7 (2013), no. 1, 3-9.
  • Peters, J. F., İnan, E. and Öztürk, M. A., Spatial and descriptive isometries in proximity spaces , General Mathematics Notes, 21 (2014), no. 2, 1-10.
  • Peters, J. F., Öztürk, M. A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science, 5 (1), 1-13, 2015.
  • Száz, A., Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50 (1987), no. 3-4, 177-201, MR0918156.
There are 19 citations in total.

Details

Primary Language English
Journal Section Review Articles
Authors

Ebubekir İnan 0000-0002-7269-8941

Publication Date February 1, 2019
Submission Date November 16, 2017
Acceptance Date February 28, 2018
Published in Issue Year 2019 Volume: 68 Issue: 1

Cite

APA İnan, E. (2019). Approximately Groups in Proximal Relator Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 572-582. https://doi.org/10.31801/cfsuasmas.438380
AMA İnan E. Approximately Groups in Proximal Relator Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2019;68(1):572-582. doi:10.31801/cfsuasmas.438380
Chicago İnan, Ebubekir. “Approximately Groups in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, no. 1 (February 2019): 572-82. https://doi.org/10.31801/cfsuasmas.438380.
EndNote İnan E (February 1, 2019) Approximately Groups in Proximal Relator Spaces. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 572–582.
IEEE E. İnan, “Approximately Groups in Proximal Relator Spaces”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 68, no. 1, pp. 572–582, 2019, doi: 10.31801/cfsuasmas.438380.
ISNAD İnan, Ebubekir. “Approximately Groups in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (February 2019), 572-582. https://doi.org/10.31801/cfsuasmas.438380.
JAMA İnan E. Approximately Groups in Proximal Relator Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:572–582.
MLA İnan, Ebubekir. “Approximately Groups in Proximal Relator Spaces”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 68, no. 1, 2019, pp. 572-8, doi:10.31801/cfsuasmas.438380.
Vancouver İnan E. Approximately Groups in Proximal Relator Spaces. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):572-8.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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