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Euclidean Locality in Treonic Topological Spaces: The Genesis of Treonic Manifolds
Version 1
: Received: 30 July 2024 / Approved: 31 July 2024 / Online: 31 July 2024 (14:13:20 CEST)
How to cite: Bermejo Valdés, A. J. Euclidean Locality in Treonic Topological Spaces: The Genesis of Treonic Manifolds. Preprints 2024, 2024072551. https://doi.org/10.20944/preprints202407.2551.v1 Bermejo Valdés, A. J. Euclidean Locality in Treonic Topological Spaces: The Genesis of Treonic Manifolds. Preprints 2024, 2024072551. https://doi.org/10.20944/preprints202407.2551.v1
Abstract
We explore the concept of Euclidean locality within treonic topological spaces. Our study establishes a foundational theoretical framework, elucidating the properties of continuity, homeomorphisms, and compactness in these spaces. We assess the Euclidean locality of treonic spaces through the analysis of specific homeomorphisms, which enables us to define manifolds in treonic spaces and extend recent research on Bermejo Algebras. For the first time, we characterize treonic manifolds by incorporating the property of Euclidean locality alongside previously studied properties such as Hausdorff spaces and second countable spaces. Our findings advance the understanding of the topological and geometric properties of treonic spaces, providing significant insights for advanced mathematical research.
Keywords
treonic spaces; Euclidean locality; topological manifolds; homeomorphisms; Bermejo algebras
Subject
Computer Science and Mathematics, Geometry and Topology
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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