Z-连通连续偏序集的遗传性及不变性

Heredity and Invariance of Z-connected Continuous Posets

本文引入了Z_c-子空间的概念,证明了Z_c-连续(代数)偏序集对Z_c-闭集是可遗传的,并给出例子说明Z_c-连续偏序集的Z_c-Scott开集通常不是Z_c-连续的。最后我们证明了在特殊的连通集系统下,Z_c-连续(代数)性在既保局部基又保Z_c-集并的映射下保持不变,且Z_c-连续(代数)偏序集的收缩仍是Z_c-连续(代数)偏序集。

In this paper, we introduce the concept of Zc-subspaces, and prove that Zc-continuous （algebraic） posets are hereditary to Zc-closed sets. We also construct an example to present that the Zc-Scott open sets of Zc-continuous posets may not be Zc-continuous. Finally, we consider a special connected set system, and then prove that Zc-continuity （algebraicity） is invariant under the mapping preserving local bases and supremum of Zc-sets. We also obtain that the contractions of Zc-continuous （algebraic） posets are still Zc-continuous （algebraic） posets.