习题 16, § 6

Show that on a ring $A$ (resp. a division ring $K$), the least upper bound $\mathfrak{T}$ of a family $(\mathfrak{T}_i)$ of topologies compatible with the ring structure of $A$ (resp. the division ring structure of $K$) is compatible with this structure. 集合 $M$ 是每个拓扑的左（或右）边界 $\mathfrak{T}_i$ 也是 $\mathfrak{T}$ 的左（或右）边界。