连续dcpo上lawson拓扑的紧性

Compactness of lawson topology in continuous dcpo

由于dcpo上赋予lawson拓扑后相对于scott拓扑会用更好的性质(由于lawson拓扑细于scott拓扑)。因此人们对lawson拓扑及lawson开集都很关注。本文主要讨论了连续dcpo上lawson拓扑紧性的问题。指出即使连续dcpoD是凝聚的,也不能保证D是lawson紧的,同时给出了一些lawson拓扑紧的例子。

Compared with scott topology,there are better properties in lawson topology in continuous dcpo. So researchers usually foced on the lawson topology and lawson open sets. This paper discussed the compactness of lawson topology in continuous dcpo,presents that a continuous dcpo is coherent, but it’s not compact in lawson topology. Moreover the paper discusses some compact dcpo in lawson topology field.