稳定连续半格的闭包空间表示

A representation of stably continuous semilattices by closure spaces

为稳定连续半格构建合适的闭包空间表示,引入了可乘闭包空间的概念,证明了可乘闭包空间的正则闭集族在集合包含关系下构成了一个稳定连续半格,并且所有的稳定连续半格都可在序同构的意义下由此生成.进一步提出了可乘闭包空间之间逼近映射的概念,刻画了以Scott连续映射为态射的稳定连续半格范畴和以逼近映射为态射的可乘闭包空间范畴间的等价性.

The main purpose of this paper is to establish an appropriate representation for stably continuous semilattices by closure spaces.The notion of a multiplicative closure space is introduced.It is shown that the collection of all regular closed sets of multiplicative closure space under set inclusion forms a stably continuous semilattice and every stably continuous semilattice can be obtained in this way up to isomorphism.Moreover,the notion of an approximable mapping between multiplicative closure spaces is presented to characterize the equivalence between the category of stably continuous semilattices with Scott continuous functions and that of multiplicative closure spaces with approximable mappings.