Abstract In this paper we investigate filter topologies on MV-algebras. We give several equivalent conditions for a filter topology making an MV-algebra into a topological MV-algebra. Moreover, we determine all filter topologies on an MV-chain; in particular, it is shown that an MV-chain with a filter topology is always a topological MV-algebra. If an MV-algebra is compact and Hausdorff with respect to a filter topology, then it is a finite product of MV-chains, each of which is a finite or the standard MV-algebra.

中文翻译：

---

滤波器拓扑和拓扑 MV 代数

摘要 在本文中，我们研究了 MV 代数上的滤波器拓扑。我们给出了滤波器拓扑的几个等效条件，使 MV 代数成为拓扑 MV 代数。此外，我们确定了 MV 链上的所有滤波器拓扑；特别是，它表明具有滤波器拓扑的 MV 链始终是拓扑 MV 代数。如果一个 MV 代数是紧致的，并且相对于滤波器拓扑是 Hausdorff，那么它是 MV 链的有限乘积，每个链都是有限的或标准的 MV 代数。