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All Journal Journal of Multidisciplinary Science: MIKAILALSYS Asian Journal of Science, Technology, Engineering, and Art Mikailalsys Journal of Mathematics and Statistics
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.
A Study of Some Geometric Structures on Inner Metric Spaces Morawo, Monsuru A; F. F, Otoide; E. O, Shobanke; O. O, Adegbemi
Mikailalsys Journal of Mathematics and Statistics Vol 4 No 1 (2026): Mikailalsys Journal of Mathematics and Statistics
Publisher : Darul Yasin Al Sys

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.58578/mjms.v4i1.7869

Abstract

Inner metric spaces, characterized by the approximate midpoint property, play an important role in metric geometry and in the analysis of length structures on metric spaces. This paper investigates structural properties of inner metric spaces, focusing on the relationship between the inner metric condition, approximate midpoints, and geodesicity. We first revisit the definition of inner metric spaces and establish that every inner metric space admits an approximate midpoint. We then show that, when an inner metric space is proper, it is geodesic. The arguments rely on the notions of length of curves and rectifiable curves to relate distance and curve length within this class of spaces. These results clarify how the inner metric property is linked to geodesic behavior and contribute to a deeper understanding of metric spaces that can be treated as length spaces.
Co-Authors E. O, Shobanke F. F, Otoide Kiltho, Ahmadu O, Okoro N. O, Shobanke, E. O. O, Adegbemi Y, Azeez, K.