Research Article
BibTex RIS Cite

Exactness of Proximal Group Homomorphisms

Year 2022, Volume: 43 Issue: 4, 652 - 655, 27.12.2022

Mehmet Ali Öztürk

https://doi.org/10.17776/csj.1126326

Abstract

This research introduces groups in proximity spaces which endowed with a proximity relation. Two penultimate choices for such relations are the Efremovic (EF) proximity relation and its extension, namely, the descriptive EF-proximity relation. There is a strong relationship between sets (groups) and set (group) descriptions. Therefore, in this paper we consider this relationship via exactness of descriptive homomorphisms between ordinary descriptive groups and meta-descriptive groups. The definition of a short exact sequence of descriptive homomorphisms is given. Then, results were obtained giving the relationships between the two short exact sequences.

Keywords

Proximal group EF-proximity space Descriptive EF-proximity space Descriptive homomorphism.

Supporting Institution

-

Project Number

-

Thanks

The author wish to thank the anonymous reviewers for their valuable suggestions.

References

  • [1] Peters, J.F., İnan, E., Öztürk, M.A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes 21(2) (2014) 1-10.
  • [2] Peters, J.F., İnan, E., Öztürk, M.A., Monoids in proximal Banach spaces, Int. J. Algebra 8(18) (2014) 869-872.
  • [3] Peters, J.F., Naimpally, S., Applications of near sets, Notes of the Amer. Math. Soc. 59(4) (2012) 536-542.
  • [4] Peters, J.F., Near sets: An introduction, Math. Comput. Sci. 7(1) (2013) 3-9.
  • [5] Efremovic, V.A., The geometry of proximity I (in Russian), Mat. Sbornik N. S. 31(73) (1952) 189-200.
  • [6] Kasch, F., Modules and Rings, Academic Press Inc. Ltd., London, 1982.
  • [7] Kovar, M.M., A new causal topology and why the universe is co-compact, arXive:1112.0817 [math-ph] (2011) 1-15.
  • [8] Peters, J.F., Local near sets: Pattern discovery in proximity spaces, Math. Comput. Sci. 7(1) (2013) 87-106.
  • [9] Cech, E., Topological Spaces, John Wiley & Sons Ltd., London, 1966.
  • [10] Peters, J.F., Öztürk, M.A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science 5(1) (2015) 1-13.

Year 2022, Volume: 43 Issue: 4, 652 - 655, 27.12.2022

Mehmet Ali Öztürk

https://doi.org/10.17776/csj.1126326

Abstract

Keywords

Proximal group EF-proximity space Descriptive EF-proximity space Descriptive homomorphism.

Project Number

-

References

  • [1] Peters, J.F., İnan, E., Öztürk, M.A., Spatial and descriptive isometries in proximity spaces, Gen. Math. Notes 21(2) (2014) 1-10.
  • [2] Peters, J.F., İnan, E., Öztürk, M.A., Monoids in proximal Banach spaces, Int. J. Algebra 8(18) (2014) 869-872.
  • [3] Peters, J.F., Naimpally, S., Applications of near sets, Notes of the Amer. Math. Soc. 59(4) (2012) 536-542.
  • [4] Peters, J.F., Near sets: An introduction, Math. Comput. Sci. 7(1) (2013) 3-9.
  • [5] Efremovic, V.A., The geometry of proximity I (in Russian), Mat. Sbornik N. S. 31(73) (1952) 189-200.
  • [6] Kasch, F., Modules and Rings, Academic Press Inc. Ltd., London, 1982.
  • [7] Kovar, M.M., A new causal topology and why the universe is co-compact, arXive:1112.0817 [math-ph] (2011) 1-15.
  • [8] Peters, J.F., Local near sets: Pattern discovery in proximity spaces, Math. Comput. Sci. 7(1) (2013) 87-106.
  • [9] Cech, E., Topological Spaces, John Wiley & Sons Ltd., London, 1966.
  • [10] Peters, J.F., Öztürk, M.A., Uçkun, M., Exactness of Proximal Groupoid Homomorphisms, Adıyaman University Journal of Science 5(1) (2015) 1-13.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Natural Sciences
Authors

Mehmet Ali Öztürk 0000-0002-1721-1053

Project Number -
Publication Date December 27, 2022
Submission Date June 6, 2022
Acceptance Date September 1, 2022
Published in Issue Year 2022Volume: 43 Issue: 4

Cite

APA Öztürk, M. A. (2022). Exactness of Proximal Group Homomorphisms. Cumhuriyet Science Journal, 43(4), 652-655. https://doi.org/10.17776/csj.1126326
 Download Cover Image