广义可数逼近偏序集上的两个扩张定理

Two extension theorems on generalized countably approximating posets

广义可数逼近偏序集是可数逼近偏序集的一种推广。本文引入广义可数定向极小集并证明了广义可数定向逼近偏序集中的每个元都存在广义可数极小集,给出了保广义可数定向极小集映射的一些等价刻画,由此得到了广义可数逼近偏序集上的两个扩张定理。

The generalized countably approximating poset is a kind of generalization of the countably approximating poset. In this paper, we introduce the definition of generalized countably directed minimal set and prove that each element of the generalized countably approximating posets has a generalized countably directed minimal set. and We give some equivalent characterizations of the mapping of preserving generalized countably directed minimal set. Based on these results, we obtain two extension theorems on generalized countably approximating posets.