由邻域、远域算子定义预拓扑的方法

A method for determining pretopologies by using neighborhood operators and remote neighborhood operators

讨论了用邻域算子、远域算子确定预拓扑的方法,并证明了预拓扑空间X上全体预拓扑T(X),全体邻域算子N(X),全体远域算子R(X),存在|T(X)|=|N(X)|,|T(X)|=|R(X)|.且(N(X),≤)与(T(X),)、(R(X),≤)与(T(X),)是完备格同构.

The method of determining pretopologies by using neighborhood operators and remote neighborhood operators is discussed.It is proven that in the pretopological space of X,there are |T(X)|=|N(X)| and T(X)=R(X)among all the pretopologies,all the neighborhood operators and all the remote neighborhood operators so that they become complete lattice isomorphic.