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.

翻译：重心理代数是对凸集概念的一种抽象，由一组方程定义。我们遵循Klaus Keimel先前关于半拓扑与拓扑锥的研究（2008年）的思路，展开对半拓扑与拓扑重心理代数的研究，而后者正是半拓扑与拓扑重心理代数的特例。