Affiliation:
1. University of Mauritius
2. Université des Mascareignes
Abstract
In a T_g-space T_g = (Ω, T_g), the g-topology T_g : P (Ω) → P (Ω) can be characterized in the generalized sense by the novel g-T_g-derived, g-T_g-coderived operators g-Der_g, g-Cod_g : P (Ω) → P (Ω), respectively, giving rise to novel generalized g-topologies on Ω. In this paper, which forms the third part on the theory of
g-T_g-operators in T_g-spaces, we study the essential properties of g-Der_g, g-Cod_g : P (Ω) → P (Ω) in T_g-spaces. We show that (g-Der_g, g-Cod_g) : P (Ω) × P (Ω) → P (Ω) × P (Ω) is a pair of both dual and monotone g-T_g-operators that is (∅, Ω), (∪, ∩)-preserving, and (⊆, ⊇)-preserving relative to g-T_g-(open, closed) sets. We also show that (g-Der_g, g-Cod_g) : P (Ω) × P (Ω) → P (Ω) × P (Ω) is a pair of weaker and stronger g-T_g-operators. Finally, we diagram various relationships amongst der_g, g-Der_g, cod_g, g-Cod_g : P (Ω) → P (Ω) and present a nice application to support the overall study.
Publisher
Journal of Universal Mathematics
Reference38 articles.
1. G. Cantor, Uber die Ausdehnung eines Satzes aus der Theorie der Trigonometrischen Reihen, Math. Ann., Vol.5, pp.123-132 (1872).
2. G. Cantor, Uber Unendliche, Lineaere Punktmannigfaltigkeiten, Ibid., Vol.20, No.III, pp.113-121 (1882).
3. S. Ahmad, Absolutely Independent Axioms for the Derived Set Operator, The American Mathematical Monthly, Vol.73, No.4, pp.390-392 (1966).
4. A. Baltag and N. Bezhanishvili and A. Ozgun and S. Smets, A Topological Apprach to Full Belief, Journal of Philosophical Logic, Vol.48, No.2, pp.205-244 (2019).
5. M. Caldas and S. Jafari and M. M. Kov_ar, Some Properties of _-Open Sets, Divulgaciones Matem_aticas, Vol.12, No.2, pp.161-169 (2004).