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Approximately Subgroups in Proximal Relator Spaces

Year 2018, Volume: 8 Issue: 1, 24 - 41, 30.06.2018

Abstract

The focus of this article is on descriptive approximately subgroups and their
homomorphisms in digital images endowed with descriptive proximity relations. Furthermore,
descriptive approximately cosets, normal subgroups, homomorphisms of descriptive
approximately groups and homomorphism theorems on descriptive approximately groups were
introduced using non-abstract points that is pixels in digital images.

References

  • [1] Clifford A., Preston G., The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., xv+224pp, 1964.
  • [2] Efremovic ̆ V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N.S.) 76, 341-343, in Russian, 1951.
  • [3] Efremovic ̆ V. A., The geometry of proximity I (in Russian), Mat. Sb. (N.S.) 31(73) (1), 189-200, 1952.
  • [4] İnan E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1), 572-582, 2019 (Available online: June 21, 2018).
  • [5] İnan E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17, 479-487, 2017.
  • [6] Kovăr M., A new causal topology and why the universe is co-compact, arXive:1112.0817[math-ph] 1-15arXiv:1112.0817, 2011.
  • [7] Lodato M. On topologically induced generalized proximity relations, Ph.D. thesis, Rutgers University, 1962.
  • [8] Naimpally S. A., Peters J. F. Topology with Applications, Topological Spaces via Near and Far. World Scientific, Singapore, 2013.
  • [9] Peters J. F., Near sets: An introduction, Math. in Comp. Sci. 7 (1), 3-9, 2013.
  • [10] Peters J. F., Naimpally S. A. Applications of near sets. Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
  • [11] Peters J. F. Proximal relator spaces, Filomat ,30 (2), 469-472, 2016.
  • [12] Peters J. F., Computational proximity. Excursions in the topology of digital images, Intelligent Systems Reference Library 102, Springer, 2016, viii + 445pp., DOI: 10.1007/978-3-319-30262-1.
  • [13] Peters J. F., Öztürk M. A. and Uçkun M., Klee-phelps convex groupoids, Math. Slovaca 67, no. 2, 397-400, 2017. DOI: doi.org/10.1515/ms-2016-0276, Zbl 06725895, MR3652277.
  • [14] Peters, J. F., Öztürk, M. A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science, 5 (1), 1-13, 2015.
  • [15] Peters J. F., İnan E., Öztürk M. A. Spatial and descriptive isometries in proximity spaces, General Mathematics Notes 21 (2), 1-10, 2014.
  • [16] Szaz A. Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50, 177-201, 1987.

Proksimal Relator Uzaylarında Yaklaşımlı Alt Gruplar

Year 2018, Volume: 8 Issue: 1, 24 - 41, 30.06.2018

Abstract

Bu makalede tanımsal proksimiti bağıntıları ile donatılmış dijital görüntülerde tanımsal yaklaşımlı alt grupların ve homomorfizmaların tanımlanması amaçlanmıştır. Ayrıca, soyut olmayan noktalar, yani dijital görüntülerdeki pikseller kullanılarak tanımlanan tanımsal yaklaşımlı gruplar üzerinde tanımsal yaklaşımlı kosetler, normal alt gruplar, tanımsal yaklaşımlı grupların homomorfizmaları ve homomorfizma teoremleri verilmiştir.

References

  • [1] Clifford A., Preston G., The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., xv+224pp, 1964.
  • [2] Efremovic ̆ V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N.S.) 76, 341-343, in Russian, 1951.
  • [3] Efremovic ̆ V. A., The geometry of proximity I (in Russian), Mat. Sb. (N.S.) 31(73) (1), 189-200, 1952.
  • [4] İnan E., Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68 (1), 572-582, 2019 (Available online: June 21, 2018).
  • [5] İnan E., Approximately semigroups and ideals: an algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering, 17, 479-487, 2017.
  • [6] Kovăr M., A new causal topology and why the universe is co-compact, arXive:1112.0817[math-ph] 1-15arXiv:1112.0817, 2011.
  • [7] Lodato M. On topologically induced generalized proximity relations, Ph.D. thesis, Rutgers University, 1962.
  • [8] Naimpally S. A., Peters J. F. Topology with Applications, Topological Spaces via Near and Far. World Scientific, Singapore, 2013.
  • [9] Peters J. F., Near sets: An introduction, Math. in Comp. Sci. 7 (1), 3-9, 2013.
  • [10] Peters J. F., Naimpally S. A. Applications of near sets. Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
  • [11] Peters J. F. Proximal relator spaces, Filomat ,30 (2), 469-472, 2016.
  • [12] Peters J. F., Computational proximity. Excursions in the topology of digital images, Intelligent Systems Reference Library 102, Springer, 2016, viii + 445pp., DOI: 10.1007/978-3-319-30262-1.
  • [13] Peters J. F., Öztürk M. A. and Uçkun M., Klee-phelps convex groupoids, Math. Slovaca 67, no. 2, 397-400, 2017. DOI: doi.org/10.1515/ms-2016-0276, Zbl 06725895, MR3652277.
  • [14] Peters, J. F., Öztürk, M. A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science, 5 (1), 1-13, 2015.
  • [15] Peters J. F., İnan E., Öztürk M. A. Spatial and descriptive isometries in proximity spaces, General Mathematics Notes 21 (2), 1-10, 2014.
  • [16] Szaz A. Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50, 177-201, 1987.
There are 16 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Ebubekir İnan 0000-0002-7269-8941

Publication Date June 30, 2018
Submission Date February 11, 2018
Acceptance Date June 5, 2018
Published in Issue Year 2018 Volume: 8 Issue: 1

Cite

APA İnan, E. (2018). Approximately Subgroups in Proximal Relator Spaces. Adıyaman University Journal of Science, 8(1), 24-41.
AMA İnan E. Approximately Subgroups in Proximal Relator Spaces. ADYU J SCI. June 2018;8(1):24-41.
Chicago İnan, Ebubekir. “Approximately Subgroups in Proximal Relator Spaces”. Adıyaman University Journal of Science 8, no. 1 (June 2018): 24-41.
EndNote İnan E (June 1, 2018) Approximately Subgroups in Proximal Relator Spaces. Adıyaman University Journal of Science 8 1 24–41.
IEEE E. İnan, “Approximately Subgroups in Proximal Relator Spaces”, ADYU J SCI, vol. 8, no. 1, pp. 24–41, 2018.
ISNAD İnan, Ebubekir. “Approximately Subgroups in Proximal Relator Spaces”. Adıyaman University Journal of Science 8/1 (June 2018), 24-41.
JAMA İnan E. Approximately Subgroups in Proximal Relator Spaces. ADYU J SCI. 2018;8:24–41.
MLA İnan, Ebubekir. “Approximately Subgroups in Proximal Relator Spaces”. Adıyaman University Journal of Science, vol. 8, no. 1, 2018, pp. 24-41.
Vancouver İnan E. Approximately Subgroups in Proximal Relator Spaces. ADYU J SCI. 2018;8(1):24-41.

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