中文摘要：

广义可数逼近偏序集是可数逼近偏序集的一种推广。本文证明了可数定向完备偏序集为广义可数逼近偏序集当且仅当其上由广义σ-理想诱导的映射有下伴随;广义可数逼近偏序集中有限生成上集之集族在反包含序下构成的偏序集为可数逼近偏序集。

英文摘要：

Generalized countably approximating posets is a kind of generalization of countably approximating posets. In this paper, we prove that （1） A poset P with countably directed joins is a generalized eountably approximating poset if and only if the mapping induced by the generalized a-ideals on P has a lower adjoint, and （2） The finitely generated upper sets on P is countably approximating poset under the order of reverse inclusion.