Article
Version 1
This version is not peer-reviewed
Hausdorff Spaces in Bermejo Algebras: The Birth of Treonic Manifold Construction
Version 1
: Received: 10 July 2024 / Approved: 11 July 2024 / Online: 11 July 2024 (16:33:54 CEST)
How to cite: Bermejo Valdés, A. J. Hausdorff Spaces in Bermejo Algebras: The Birth of Treonic Manifold Construction. Preprints 2024, 2024070940. https://doi.org/10.20944/preprints202407.0940.v1 Bermejo Valdés, A. J. Hausdorff Spaces in Bermejo Algebras: The Birth of Treonic Manifold Construction. Preprints 2024, 2024070940. https://doi.org/10.20944/preprints202407.0940.v1
Abstract
We conducted a topological analysis of the novel, non-associative, and unital algebraic structure known as Bermejo Algebras, developed by Alejandro Bermejo, which includes the Algebra B and Treon Algebra. This algebras can define Lie and Malcev algebras when their product operations are derived from the Bermejo Algebras product. Central to this study are treons, complex entities that arise as isomorphisms of Algebra B when the field is real. We define the vector spaces associated with Bermejo Algebras to establish equivalence classes and a quotient topology, resulting in Hausdorff spaces that do not depend on traditional norms, inner products, or metrics. Our findings lay the groundwork for constructing new types of differential manifolds, opening new avenues for advanced mathematical research.
Keywords
Bermejo Algebra; Treons; Algebra B; Topology; Hausdorff Space
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.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
