关于弱网与拟网及其子网的一些探究

Some Explorations on the Weak and Proposed Networks and Their Subnets

摘要: 讨论了可数个各类定向集乘积序的性质，得到了可数个弱定向集(拟定向集，定向集)的乘积也是弱定向(拟定向集，定向集)的这一结果。引入拟网与弱网接触点以及收敛的概念，由此探究了拟网与其拟子网(弱子网)之间的联系，对拟网与弱网收敛性进行了更为深刻的刻画，证明了拟网(弱网)关于紧空间的一个收敛结果；提出了严格拟定向集和严格弱定向集这一概念，在此基础上推广到严格拟网以及严格弱网，对各类型网与子网的关系进行了刻画。

Abstract: This paper discusses the nature of the product sequence of several kinds of directional sets, and obtains the result that the product of several weak directional sets (proposed set, directional set) is also weakly oriented (proposed set, directional set). The concept of the contact point and con-vergence between the proposed net and the weak net is introduced, thus the connection between the proposed net and its proposed subnet (weak subnet) is explored, the convergence between the proposed net and the weak net is depicted more deeply, and the convergence result of the proposed net (weak net) is proved to be a convergence of tight space.