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Approximately Groups in Proximal Relator Spaces

Year 2019, , 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, , 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

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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