Advancing Neutrosophic Topology through b-Open Sets and their Application to Neutrosophic b-Compact Spaces

Entsar El Amin

doi:10.54172/t7dmaa92

Authors

Entsar El Amin Department of Mathematics, Faculty of Science, Al-zawia University, Libya. Author

DOI:

https://doi.org/10.54172/t7dmaa92

Keywords:

neutrosophic b-open sets, neutrosophic subspaces, neutrosophic b -compact spaces.

Abstract

The main objective of this study is to develop a neutrosophic topology by applying topological mechanisms to establish an induced neutrosophic topology and new topological spaces known as neutrosophic subspaces. In addition, we apply specific topological tools to neutrosophic concepts (open neutrosophic sets of type b) and study the properties of this type of neutrosophic openness. The resulting space, which does not satisfy the three topological conditions but is limited to a supra topology, is called a neutrosophic b supra topological space, and we investigate its main properties. Based on this framework, the concept of b neutrosophic compactness is developed as a natural generalization of compactness in neutrosophic spaces. We establish that every b-compact neutrosophic space is a compact neutrosophic space, but the converse is not true. The research also examines how b-compactness behaves under various mappings, such as continuous and open neutrosophic functions, such as connected and open neutrosophic functions. Furthermore, the research also shows that every neutrosophic supra b-compact space is neutrosophic supra compact and neutrosophic b-compact. The results show that neutrosophic b-compactness serves as a flexible and powerful tool capable of describing and explaining real-world phenomena that are predominantly characterized by uncertainty. Accordingly, this approach reinforces the foundations of neutrosophic topology, which increases its applicability in data analysis, leading to decisions that are more precise.

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