关于R({0,1/2,1})的水平拓扑的一个结果

A result of level topological spaces of R({0,1/2,1})

设L={0,1/2,1},Reg(XL)是L-实直线(R(L),δ)的水平拓扑空间(R(L),lL,1/2(δ))中的正则开集的全体.利用R(L)与平面R2的子集XL={〈r,s〉∈R2|r≤s}之间的序同构关系,证明了(Reg(XL),)是有补的locale,但它无素元,无余素元且不满足完全分配律.

Let L={0,1/2,1},Reg（XL） is the set of all regular open sets in （R（L）,lL,1/2（δ）） （a level space of L-real line （R（L）,δ））. By using the order isomorphism between R（L） and XL = {（r,s）∈R^2r ≤s} （a subset of R2）, it is proved that （Reg（XL）, C） is a locale which has complementary operation, but has neither prime element nor coprime element, which is not a completely distributive complete latrice too.