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Y, Azeez, K.
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Some Studies on the Topology of Power Set Morawo, Monsuru A; Kiltho, Ahmadu; Y, Azeez, K.; O, Shobanke, E.; O, Okoro N.
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 2 (2025): Journal of Multidisciplinary Science: MIKAILALSYS
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mikailalsys.v3i2.6328

Abstract

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.
Co-Authors Kiltho, Ahmadu Morawo, Monsuru A O, Okoro N. O, Shobanke, E.