@article{Oudetallah2026, 
author = {Jamal Oudetallah and Ala Amourah and Abdullah Alsoboh and Jamal Salah and Tala Sasa},
title = {Ω-sequential compactness and orbital connectedness in tri-topological spaces},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {7},
pages = {22401-22409},
keywords = {Ω-sequential compactness, multi-topological spaces, tri-topological spaces},
url = {https://www.sciopen.com/article/10.3934/math.2026906},
doi = {10.3934/math.2026906},
abstract = {We introduce and study two novel topological invariants in the context of tri-topological spaces:    Ω-sequential compactness and orbital connectedness. Unlike the classical approach to multi-topological spaces, we define tri-topological spaces through an interaction function    ρ  :      τ    1    ×      τ    2    →      P    (  X  ) that encodes sophisticated relationships among three topologies. These invariants extend classical notions of sequential compactness and path connectedness, providing powerful tools for distinguishing tri-topological spaces. We establish fundamental theorems regarding their preservation under tri-continuous mappings, behavior in tri-product spaces, and relationships with classical topological properties. Additionally, we develop new tri-separation axioms based on these invariants and provide illustrative examples demonstrating their independence from standard properties.}
}