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All Journal Journal of Multidisciplinary Science: MIKAILALSYS Asian Journal of Science, Technology, Engineering, and Art
Morawo, Monsuru A
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Relatively Compactness on Some Hyperspaces Associated with Riemannian Manifolds Morawo, Monsuru A
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.v3i2.5062

Abstract

In this paper, we defined relatively compactness on hyperspaces CL(X) and C(X) of Riemannian metric space and relatively compactness theorem about metric spaces in the Gromov sense. Some classes of Riemannian manifolds as applications were defined.
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.
A Study on Homotopy Invariance of Circle and Stereographic Projection Morawo, Monsuru A
Journal of Multidisciplinary Science: MIKAILALSYS Vol 3 No 3 (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.v3i3.6866

Abstract

This paper explores fundamental applications of topological spaces and stereographic projection derived from the properties of the circle, employing key concepts such as continuous functions and homotopy theory. By examining the behavior of mappings and deformations within topological spaces, the study demonstrates how the circle serves as a foundational structure for understanding more complex topological constructs. Special attention is given to the use of stereographic projection in visualizing the relationship between the circle and the unit sphere, illustrating how these mathematical tools contribute to a deeper understanding of continuity and homotopy in topological analysis. The discussion offers a concise yet insightful introduction to the interplay between geometric intuition and topological formalism.
Co-Authors Kiltho, Ahmadu O, Okoro N. O, Shobanke, E. Y, Azeez, K.