中文摘要：

讨论了C-双有限domain的SM性质，并证明：（i）所有 C-双有限 domain 具有 SM性质；（ii）连续L-domain D是C-双有限domain 当且仅当D具有SM性质当且仅当D上存在基B使得其理想完备化Id（B）是双有限domain.

英文摘要：

we consider the SM property of C-bifinite domains and show that （i）every C-bifinite domain has SM property;（ii）a continuous L-domain D is a C-bifinite domain if and only if it has SM property if and only if it has a basis B such that its ideal completeness Id（B）is a bifinite domain.