Construction of a Second-Countable Treon Space From a New Metric Structure

Alejandro Jesús Bermejo Valdés

doi:10.20944/preprints202407.1483.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 17 July 2024 / Approved: 18 July 2024 / Online: 18 July 2024 (10:31:03 CEST)

Bermejo Algebras, which consist of Algebra B and Treon Algebra, are non-associative and unital algebraic structures that introduce new complex entities. Recently, a Hausdorff space associated with the space where these algebras act was defined. We constructed a second-countable treon space utilizing a novel metric derived from these algebras. We defined topological spaces and established a metric to prove the second-countable property within Bermejo Algebras. Our findings contribute to the construction of manifolds in treon spaces by defining a countable base using the density of rationals in the real numbers.

Bermejo Algebras; Treon Algebra; second-countable space; metric topology; manifolds

Computer Science and Mathematics, Geometry and Topology

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Construction of a Second-Countable Treon Space From a New Metric Structure

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