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All Journal Journal of Multidisciplinary Science: MIKAILALSYS Asian Journal of Science, Technology, Engineering, and Art
Y., Azeez K.
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Agriculture, Biological Sciences & Forestry Arts Chemical Engineering, Chemistry & Bioengineering Computer Science & IT Engineering Environmental Science Physics Social Sciences Other

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Gromov - Hausdorff Dimension and Measure of Separable Metric Spaces Morawo, Monsuru A.; D., Hina A.; Y., Azeez K.
Asian Journal of Science, Technology, Engineering, and Art Vol 3 No 2 (2025): Asian Journal of Science, Technology, Engineering, and Art
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/ajstea.v3i2.5206

Abstract

In this paper, we proved that dimension of Gromov – Hausdorff hyperspace of Riemannian manifold depends on the cardinality of measurable Riemannian manifold.
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.v3i2.6099

Abstract

This paper investigates the topological structure of the power set of an infinite set XX, focusing on properties such as extreme and total disconnectedness, as well as the hierarchy of separation axioms τ0,τ1,τ2,τ3,τ4,τ5,τ6\tau_0, \tau_1, \tau_2, \tau_3, \tau_4, \tau_5, \tau_6. By defining a topology on the power set, the study explores how classical topological concepts manifest in this context and introduces a novel perspective that bridges the power set with a Universal Topological Space. The analysis contributes to a deeper understanding of how separation properties and disconnectedness behave in non-traditional topological constructions, offering a foundational approach for further exploration in abstract topological frameworks.
Co-Authors D., Hina A. Kiltho, Ahmadu Morawo, Monsuru A. O., Okoro N. O., Shobanke E.