偏序集上的MS-收敛

MS-convergence on posets

定义在s_(2)-连续偏序集上的S-极限是一种重要的收敛结构.本文用集族MS代替定向集,将s_(2)-连续和S-极限进行推广,定义了s_(2)MS-连续和MS-极限,并用MS-极限定义了s_(2)MS-α-连续.本文主要结果有:(i)如果L为s_(2)MS-连续偏序集且MS关系具有插入性质,则MS-收敛是拓扑的;(ii)如果L为偏序集,任意的x∈L,α(MS)x∈MS且α(MS)具有插入性质,则MS-收敛为拓扑的当且仅当L为s_(2)MS-α-连续的.

S-limit defined on s 2-continuous posets is an important convergence structure.In this paper,we define s 2MS-continuous posets and MS-limit by replacing the directed set with set family.Meanwhile,we also define the s 2MS-α-continuous posets with MS-limit.The main results are as follows.(i)Let L be s 2MS-continuous poset and MS relationship has the insertion property,then the MS-limit is topological.(ii)Let L be a poset.If for any x∈L,α(MS)x∈MS andα(MS)has the insertion property,then MS-limit is topological if and only if L is s 2MS-α-continuous.