Semitopological Barycentric Algebras
arXiv:2512.1286525.6
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For researchers in universal algebra and topology, this work generalizes known results, but it is incremental as it follows the template of Keimel's work on cones.
The paper extends the study of semitopological and topological structures from cones to barycentric algebras, establishing foundational results for these more general algebraic structures.
Barycentric algebras are an abstraction of the notion of convex sets, defined by a set of equations. We study semitopological and topological barycentric algebras, in the spirit of a previous study by Klaus Keimel on semitopological and topological cones (2008), which are special cases of semitopological and topological barycentric algebras.