积闭集

We firstly discuss minimal sets characterizations of closed-set lattice , then systematically study the categorical properties of categories CL and PairCL by the means of the join-semilattices closed-set-latticefies, and the constructions of monomorphism, epimor-phism, extremal monomorphism, extremal epimorphism, section, retraction, subob-ject, quotient object, product, co-product, equalizer, coequalizer, inverse limits and direct limits in the categories CL and PairCL are given.

首先讨论了闭集格的极小集刻划，然后通过并半格的闭集格化这种方法，较为系统地研究了范畴CL及范畴PairCL的性质，给出了范畴CL和范畴PairCL的单态射、满态射、极端单态射、极端满态射、截节、收缩、子对象、商对象、极端子对象、极端商对象等特殊态射和特殊对象的具体刻划，并且研究了它们的等化子和余等化子、乘积和余积、逆极限和定向极限的具体构造。

We firstly discuss minimal sets characterizations of closed-set lattice , then systematically study the categorical properties of categories CL and PairCL by the means of the join-semilattice's closed-set-latticefies, and the constructions of monomorphism, epimor-phism, extremal monomorphism, extremal epimorphism, section, retraction, subob-ject, quotient object, product, co-product, equalizer, coequalizer, inverse limits and direct limits in the categories CL and PairCL are given.

首先讨论了闭集格的极小集刻划，然后通过并半格的闭集格化这种方法，较为系统地研究了范畴CL及范畴PairCL的性质，给出了范畴CL和范畴PairCL的单态射、满态射、极端单态射、极端满态射、截节、收缩、子对象、商对象、极端子对象、极端商对象等特殊态射和特殊对象的具体刻划，并且研究了它们的等化子和余等化子、乘积和余积、逆极限和定向极限的具体构造。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。