Z-完备偏序集上诱导的拓扑

Induced Z-Scott topology on Z-complete posets

在Z-完备偏序集中引入诱导拓扑概念,找到了诱导拓扑的一个基,并给出了它一个相应的等价刻画;同时证明了诱导拓扑映射是可以复合并且是严格单调的。

The definition of induced Z-Scott topology was introduced and a basis of induced topology was found based on Z-complete posets.Some equivalent characterizations of induced Z-Scott topology were ob-tained as well.It discussed the properties of induced Z-Scott topology and proved that the induced topology mapping could be composed to yield the strict monotonicity.