Semitopological $\delta$-groups

Abstract

The aim of this paper is to introduce semitopological $\delta$-group and topological $\delta$-group with the concept of $\delta$-group which arise from approximately algebraic structures. Furthermore, it is shown that product space determined with $\delta$-topological subspaces is a $\delta$-topological space. Fundamental system of open $\delta$-neighborhoods and related properties were investigated.

Keywords

• topological group
• approximately group
• proximity space

References

1. [1] A. Di Concilio, C. Guadagni, J. F. Peters and S. Ramanna, Descriptive Proximities: Properties and interplay between classical proximities and overlap, Mathematics in Computer Science 12 (1), 91-106, 2018.
2. [2] V. A. Efremovič, Infinitesimal spaces, Doklady Akad. Nauk SSSR (N. S.) (Russian) 76, 341-343, 1951.
3. [3] V. A. Efremovič, The geometry of proximity I, Mat. Sb. (N. S.) (Russian) 31 (73), 189-200, 1952.
4. [4] T. Husein, Introduction to Topological Groups, W.B. Sauders Company, 1966.
5. [5] E. İnan, Approximately semigroups and ideals: An algebraic view of digital images, Afyon Kocatepe University Journal of Science and Engineering 17, 479-487, 2017.
6. [6] E. İnan, Approximately subgroups in proximal relator spaces, Adıyaman University Journal of Science 8 (1), 24-41, 2018.
7. [7] E. İnan, Approximately groups in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (1), 572-582, 2019.
8. [8] E. İnan, Approximately rings in proximal relator spaces, Turkish J. Math. 43, 2941- 2953, 2019.

9. [9] E. İnan and M. Uçkun, Approximately $\Gamma$-semigroups in proximal relator spaces, Appl. Algebra Eng. Commun. Comput. 30 (4), 299-311, 2019.
10. [10] M. Kovăr, A new causal topology and why the universe is co-compact, arXiv: 1112.0817 [math-ph], 1-15, 2011.
11. [11] S. A. Naimpally and J. F. Peters, Topology with Applications: Topological Spaces via Near and Far, World Scientific, 2013.
12. [12] S. A. Naimpally and B. D. Warrack, Proximity Spaces, Cambridge University Press, 1970.
13. [13] J. F. Peters and S. A. Naimpally, Applications of near sets, Notices Amer. Math. Soc. 59 (4), 536-542, 2012.
14. [14] M. Uçkun, Approximately $\Gamma$-rings in proximal relator spaces, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 68 (2), 1780-1796, 2019.