Some Studies on the Topology of Power Set - Monsuru A Morawo; Ahmadu Kiltho; Azeez, K. Y; Shobanke, E. O; Okoro N. O (Journal of Multidisciplinary Science: MIKAILALSYS, 2025)
This paper examines the topological structure of the power set of an infinite set X, with a focus on properties such as extreme and total disconnectedness, as well as the hierarchy of separation axioms T₀, T₁, T₂, T₃, T₄, T₅, and T₆. By defining a topology τ on the power set ????(X), the study explores the manifestation of classical topological properties within this framework. The investigation introduces a novel approach that connects ????(X) to a universal topological space, providing new insights into the behavior of separation axioms and disconnectedness in non-standard topological constructions. The results offer a foundational perspective for further study in abstract and generalized topology, particularly in contexts where conventional space constructions do not apply.