caccc半序集及其不动点性质

Caccc poset and the fixed point property

旨在寻找 caccc半序集 P的一个新子集合 ,使这个集合的不动点性质与 P的不动点性质一致。采用了序集理论中的不动点方法。证明了若 P是 cac半序集 ,则 D( P) ={x∈ P:存在 -极大元 y,满足 y x}=P,并对李伯渝的论文“The anti- order for caccc posets”( DiscreteMathematics,1 996,1 58:1 73- 1 84)

The purpose is to find a new subset of caccc poset P .The new subset has the same fixed point property as caccc poset P . Use the method of the fixed point in the orded sets theory. It is proved that if P is a cac poset, then D(P)=｛x∈P :there is a  maximal element y such as xy｝=P . The results and proofs of the theorems in the thesis 'The anti order for caccc posets' (LI Bo yu,Discrete Mathematics, 1996,158:173 184) are simplified.