关于用边界算子定义拓扑空间的讨论

关于拓扑空间的定义有多种形式，有别于传统的方法，本文利用边界算子定义了拓扑空间，给出了完整的证明，还对边界算子的特征性质进行了讨论；最后，将边界算子的特征性质归结为一条，所采用的方法具有一定的创新性，所得结论丰富了拓扑空间的理论基础。

A Discussion of Definition to the Topological Space by Applying Boundary Operators

There have been definitions of many forms to the topological space, that, however, differ from a traditional one. The paper presents a definition to the topological space by means of applying boundary operators. The space defined has been fully and completely proved and certificated. Hereupon, a further discussion is carried out together with characteristic nature of the boundary operators, which have been reduced to one clause. The method herein used is of creativeness. The conclusion reached is also of real plenitude to the theoretical basis about topological space.