偏序集乘积的拓扑与拓扑乘积

The topologies of products and the topological products of posets

作者讨论了偏序集乘积的下拓扑、Scott拓扑及Lawson拓扑与它们各自对应的拓扑集积之间的关系,给出了乘积的下拓扑空间等于下拓扑乘积空间和乘积的Lawson拓扑空间等于Lawson拓扑乘积空间的充分必要条件,修正了专著《Continuous Lattices and Domains》的若干不正确的结论.

In this paper, the authors investigate the realtions among the lower topology, the Scott topology, the Lawson topology on the product of posets and their corresponding topological products, and obtain the suffcient and necessary conditions such that the corresponding topologies are equal to each other.