Some games via semi-generalized regular spaces

Sadek, A. R.; Karim, M. A. Abdel

doi:10.47974/JIM-1518

Open Access Research Article

Some games via semi-generalized regular spaces

^*A. R. SadekCorresponding authorsadek.r.afraa@gmail.comDepartment of MathematicsCollege of ScienceUniversity of BaghdadBaghdad, IraqView full profile → , M. A. Abdel Karimmaherjaleel89@yahoo.comDepartment of MathematicsCollege of Education for Pure Sciences (Ibn Al-Haitham)University of BaghdadBaghdad, IraqView full profile →

* Corresponding author · click or hover a name for details

pp. 863–872Vol. 26Issue 5August 2023DOI: 10.47974/JIM-1518XML

Received:: 11 May 2022
Accepted:: 09 Jun 2022
Published Online:: 15 Jul 2023
Article type:: Research Article
Language:: EN
Article no.:: JIM-1518
Pages:: 863–872

Abstract

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented.

Keywords

Games Regular space Sgopen set Semi-closed SgRspace Sg continuousfunction

Subject Classifications

14A2014M17

Acknowledgements

Obaid (49_icmas_h15)

References

[1] N. Levine, Semi-open sets and semi-continuity in topological spaces. Am Math Mon., 70, pp. 36-41 (1963).
[2] P. Bhattacharyya and B. K. Lahiri, “Semi Generalized Closed Sets in Topology”, J. Indian Math., 29.3, pp. 373-382 (1987).
[3] A. R. Sadek, J.H. Hussein, Regularity via semi- generalized open set, JAT, 12.4, pp. 4631-4635 (2020).
[4] B. J. Conway, Course in point set topology, Springer Cham Heidelberg, New York Dordrecht London, (2014).
[5] R. J. Aumann, Survey of repeated games. Essays in game theory and mathematical economics in honor of Oskar Morgenstern., 4, pp. 11- 42 (1981).
[6] F. Jordan, Consonant spaces and topological games, Topology Appl., 274, pp. 107-121, (2020).
[7] L. F. Aurichi and R. R. Dias, A minicourse on topological games, Topology Appl., 258, pp. 305-335 (2019).
[8] R. J. Mohammad and R. B. Esmaeel , Ibn Al-Haitham Jour. for Pure & Appl. Sci., 33.4., pp. 122-136, (2020).
[9] A. Schwarz, Mathematical Foundations of Quantum Field Theory, UC Davis, pp. 460 (2020).
[10] A. R. Sadek, P, PL. Compact Topological Ring, IJS, 57.4B, pp. 27542759 (2016).
[11] Shubham Sharma & Ahmed J. Obaid, Mathematical modeling, analysis and design of fuzzy logic controller for the control of ventilation systems using MATLAB fuzzy logic toolbox, Journal of Interdisciplinary Mathematics, 23:4, 843-849 (2020). DOI: 10.1080/09720502.2020.1727611.
[12] A. Kalavathi & G. Sai Sundara Krishnan, Soft g* closed and soft g*open sets in soft topological spaces, Journal of Interdisciplinary Mathematics, 19:1, 65-82 (2016), DOI: 10.1080/09720502.2015.1103110.

Views: 266Downloads: 97Citations: 4