S^(*)-收敛和局部强紧空间

S^(*)-convergence and locally hypercompact spaces

定向空间是定向完备偏序集的拓扑推广,局部强紧空间可以刻画为拟连续的定向空间.本文给出了关于局部强紧空间的一个拓扑版的Scott收敛定理.通过引入S^(*)-收敛的概念并定义有限逼近空间,本文得到以下主要结果:(i)定向空间X是局部强紧的当且仅当S_(X)^(*)-收敛是可拓扑化的;(ii)对任意T0空间X,S_(X)^(*)-收敛是可拓扑化的当且仅当X是有限逼近空间;(iii)若定向空间X上的Lawson拓扑是紧的,则X是赋予Scott拓扑的定向完备偏序集.

Locally hypercompact spaces can be characterized as quasicontinuous monotone determined spaces,where monotone determined spaces are topological extensions of dcpos in domain theory.In this paper,we give a topological version of the Scott convergence theorem for locally hypercompact spaces.By introducing the notion of S^(*)-convergence and defining the notion of finitely approximated spaces,the following main results are obtained:(i)A monotone determined space X is locally hypercompact iff S_(X)^(*)-convergence is topological;(ii)For a T0 space X,S_(X)^(*)-convergence is topological iff X is a finitely approximating space;(iii)If the Lawson topology on a monotone determined space X is compact,then X is a dcpo endowed with the Scott topology.