We show that the category of coalgebras for the compact Vietoris endofunctor $\mathbb{V}$ on the category Top of topological spaces and continuous mappings is isomorphic to the category of all modally saturated Kripke structures. Extending a result of Bezhanishvili, Fontaine and Venema, we also show that Vietoris subcoalgebras as well as bisimulations admit topological closure and that the category of Vietoris coalgebras has a terminal object.

翻译：我们显示,在表层空间和连续绘图的顶端类别中,紧凑的Veaoris 尾端为 $\ mathbb{V}$的煤星数与所有模式饱和 Kripke 结构的类别不相形见绌。 由于Bezhanishvili、Fontaine和Venema的结果,我们还显示,Veaoris 亚coalgebras 和双振动允许关闭表层,而Veagoris 煤星的类别有一个终端物体。