Approximately Subgroups in Proximal Relator Spaces

Öz

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.

Anahtar Kelimeler

• Proximity spaces,Relator spaces,Descriptive approximations,Approximately subgroups

Proksimal Relator Uzaylarında Yaklaşımlı Alt Gruplar

Öz

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.

Anahtar Kelimeler

• Proksimiti uzaylar,Relator uzaylar,Tanımsal yaklaşımlar,Yaklaşımlı alt gruplar

Kaynakça

1. [1] Clifford A., Preston G., The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., xv+224pp, 1964.
2. [2] Efremovic ̆ V. A., Infinitesimal spaces, Doklady Akad. Nauk SSSR (N.S.) 76, 341-343, in Russian, 1951.
3. [3] Efremovic ̆ V. A., The geometry of proximity I (in Russian), Mat. Sb. (N.S.) 31(73) (1), 189-200, 1952.
4. [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. [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. [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. [7] Lodato M. On topologically induced generalized proximity relations, Ph.D. thesis, Rutgers University, 1962.
8. [8] Naimpally S. A., Peters J. F. Topology with Applications, Topological Spaces via Near and Far. World Scientific, Singapore, 2013.

9. [9] Peters J. F., Near sets: An introduction, Math. in Comp. Sci. 7 (1), 3-9, 2013.
10. [10] Peters J. F., Naimpally S. A. Applications of near sets. Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
11. [11] Peters J. F. Proximal relator spaces, Filomat ,30 (2), 469-472, 2016.
12. [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. [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. [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. [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. [16] Szaz A. Basic tools and mild continuities in relator spaces, Acta Math. Hungar. 50, 177-201, 1987.