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：重心代数是凸集概念的抽象化，由一组方程定义。我们以Klaus Keimel先前关于半拓扑与拓扑锥的研究（2008）为思路，探讨半拓扑与拓扑重心代数，这些锥是半拓扑与拓扑重心代数的特例。