article · BIMA JOURNAL OF SCIENCE AND TECHNOLOGY GOMBE
This research examines the construction of discrete topological spaces within non-near-linear finite geometries. In these geometric systems, points and lines are formulated over the ring of integers modulo m. By establishing a partial order across subgeometries, the study demonstrates that these mathematical structures successfully satisfy standard topological axioms. Specific examples are presented to illustrate how these finite geometries behave under these conditions. Ultimately, the work establishes that the finite geometry under consideration, combined with the collection of its subsets known as subgeometries, forms a discrete topological space where the subgeometries themselves serve as the topology.
Topological and geometric structures provide essential theoretical foundations for advanced mathematics and computer science. Establishing connections between finite geometry defined over modular arithmetic and discrete topology helps mathematicians better understand the formal properties and behaviours of abstract discrete systems.
The abstract does not indicate an application pathway, as it focuses entirely on abstract mathematical formulations.
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This paper explores the construction of discrete topological spaces on non-near-linear finite geometries, where points and lines are defined over the ring of integers modulo m. By introducing a partial order among subgeometries, we demonstrate how such structures satisfy the axioms of topology and provide illustrative examples for specific cases such as finite geometry The geometry under discourse together with the collection of its subsets called subgeometry yields a discrete topological space with its subgeometries as topology.
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DOI: 10.64290/bima.v9i2b.1275
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