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

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.