BibTex RIS Cite

Exactness of Proximal Groupoid Homomorphisms

Year 2015, Volume: 5 Issue: 1 , 1 - 13 , 10.07.2015

James Peters , Mehmet Öztürk , Mustafa Uçkun

https://izlik.org/JA62EM42ET

Abstract

This article introduces proximal algebraic structures in descriptive proximity spaces. A descriptive proximity space is an extension of an Efremovič proximity space that contains non-abstract points describable with feature vectors. Various types of groupoids is such spaces are considered. A groupoid is a nonempty set equipped with a binary operation. A groupoid A is descriptively near a groupoid B , provided there is at least one pair of points , a in A and b in B with matching descriptions. This leads to a consideration of mappings on groupoid A into groupoid B that are descriptive homomorphisms

Keywords

Proximity relation descriptive proximity space proximal groupoid descriptive homomorphism

References

  • J. F. Peters, S. Naimpally, Notices Amer. Math. Soc., 2012, 59 (4), 536-542.
  • J. F. Peters, Math. Comput. Sci., 2013, 7 (1), 3-9.
  • V. Efremovič, Mat. Sb. (N.S.), 1952, 31 (73), 189-200.
  • E. Čech, Topological Spaces, revised Ed. by Z. Frolik and M. Katětov, John Wiley & Sons, 1966.
  • F. Hausdorff, Grundzüge der Mengenlehre, Veit and Company, 1914.
  • J. M. Smirnov, Math. Sb. (N.S.), 1952, 31 (73), 543-574; English Translation: Amer. Math. Soc. Trans. Ser., 1964, 2 (38), 5-35.
  • J. F. Peters, Fund. Inform., 2007, 75 (1-4), 407-433.
  • J. F. Peters, Appl. Math. Sci., 2007, 1 (53-56), 2609-2629.
  • S. Naimpally, J. F. Peters, Topology with Applications.
  • Topological Spaces via Near and Far, World Scientific, 2013.
  • J. F. Peters, Math. Comput. Sci., 2013, 7 (1), 87-106.
  • J. F. Peters, Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces, Springer-Verlag, 2014.
  • A. Clifford, G. Preston, The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., 1964.
  • J. F. Peters, E. İnan, M. A. Öztürk, Gen. Math. Notes, 2014, 21 (2), 125-134.
  • M. Kovár, arXive:1112.0817 [math-ph], 2011, 1-15.

Proksimal Grupoid Homomorfizmalarının Tamlığı

Year 2015, Volume: 5 Issue: 1 , 1 - 13 , 10.07.2015

James Peters , Mehmet Öztürk , Mustafa Uçkun

https://izlik.org/JA62EM42ET

Abstract

Bu çalışmada tanımsal proksimiti uzayda proksimal cebirsel yapılar tanıtıldı. Tanımsal
proksimiti uzay, özellik vektörleri ile nitelendirilebilen ve soyut olmayan noktaları içeren
Efremovič proksimiti uzayının bir genelleştirilmişidir. Grupoidlerin farklı türleri böyle
düşünülen uzaylardır. Grupoid, bir ikili işlem ile donatılmış boş olmayan bir kümedir. A ve
B iki grupoid olmak üzere, eşleşen tanımlamalar ile en az bir a, b nokta çifti varsa,
A grupoidi B grupoidine tanımsal yakındır. Bu kavram, A grupoidinden B grupoidine
dönüşümleri ve özellikle tanımsal homomorfizmaları göz önünde bulundurmamıza yol açar. 

Keywords

Proksimiti bağıntı tanımsal proksimiti uzay proksimal grupoid tanımsal homomorfizma.

References

  • J. F. Peters, S. Naimpally, Notices Amer. Math. Soc., 2012, 59 (4), 536-542.
  • J. F. Peters, Math. Comput. Sci., 2013, 7 (1), 3-9.
  • V. Efremovič, Mat. Sb. (N.S.), 1952, 31 (73), 189-200.
  • E. Čech, Topological Spaces, revised Ed. by Z. Frolik and M. Katětov, John Wiley & Sons, 1966.
  • F. Hausdorff, Grundzüge der Mengenlehre, Veit and Company, 1914.
  • J. M. Smirnov, Math. Sb. (N.S.), 1952, 31 (73), 543-574; English Translation: Amer. Math. Soc. Trans. Ser., 1964, 2 (38), 5-35.
  • J. F. Peters, Fund. Inform., 2007, 75 (1-4), 407-433.
  • J. F. Peters, Appl. Math. Sci., 2007, 1 (53-56), 2609-2629.
  • S. Naimpally, J. F. Peters, Topology with Applications.
  • Topological Spaces via Near and Far, World Scientific, 2013.
  • J. F. Peters, Math. Comput. Sci., 2013, 7 (1), 87-106.
  • J. F. Peters, Topology of Digital Images. Visual Pattern Discovery in Proximity Spaces, Springer-Verlag, 2014.
  • A. Clifford, G. Preston, The Algebraic Theory of Semigroups, American Mathematical Society, Providence, R.I., 1964.
  • J. F. Peters, E. İnan, M. A. Öztürk, Gen. Math. Notes, 2014, 21 (2), 125-134.
  • M. Kovár, arXive:1112.0817 [math-ph], 2011, 1-15.
There are 15 citations in total.

Details

Primary Language English
Subjects Engineering
Authors

James Peters

Mehmet Öztürk

Mustafa Uçkun

Submission Date July 10, 2015
Publication Date July 10, 2015
IZ https://izlik.org/JA62EM42ET
Published in Issue Year 2015 Volume: 5 Issue: 1

Cite

APA Peters, J., Öztürk, M., & Uçkun, M. (2015). Exactness of Proximal Groupoid Homomorphisms. Adıyaman University Journal of Science, 5(1), 1-13. https://izlik.org/JA62EM42ET
AMA 1.Peters J, Öztürk M, Uçkun M. Exactness of Proximal Groupoid Homomorphisms. ADYU J SCI. 2015;5(1):1-13. https://izlik.org/JA62EM42ET
Chicago Peters, James, Mehmet Öztürk, and Mustafa Uçkun. 2015. “Exactness of Proximal Groupoid Homomorphisms”. Adıyaman University Journal of Science 5 (1): 1-13. https://izlik.org/JA62EM42ET.
EndNote Peters J, Öztürk M, Uçkun M (June 1, 2015) Exactness of Proximal Groupoid Homomorphisms. Adıyaman University Journal of Science 5 1 1–13.
IEEE [1]J. Peters, M. Öztürk, and M. Uçkun, “Exactness of Proximal Groupoid Homomorphisms”, ADYU J SCI, vol. 5, no. 1, pp. 1–13, June 2015, [Online]. Available: https://izlik.org/JA62EM42ET
ISNAD Peters, James - Öztürk, Mehmet - Uçkun, Mustafa. “Exactness of Proximal Groupoid Homomorphisms”. Adıyaman University Journal of Science 5/1 (June 1, 2015): 1-13. https://izlik.org/JA62EM42ET.
JAMA 1.Peters J, Öztürk M, Uçkun M. Exactness of Proximal Groupoid Homomorphisms. ADYU J SCI. 2015;5:1–13.
MLA Peters, James, et al. “Exactness of Proximal Groupoid Homomorphisms”. Adıyaman University Journal of Science, vol. 5, no. 1, June 2015, pp. 1-13, https://izlik.org/JA62EM42ET.
Vancouver 1.James Peters, Mehmet Öztürk, Mustafa Uçkun. Exactness of Proximal Groupoid Homomorphisms. ADYU J SCI [Internet]. 2015 Jun. 1;5(1):1-13. Available from: https://izlik.org/JA62EM42ET

...