关于拓扑空间中某些运算产生的集合个数

About Amount of Sets Resulted by Some Operations In Topological Space

证明了拓扑空间的任意子集经过取补集、闭包和边界运算至多产生 34个集合 ,并且在实数空间上找到了一个子集 ,由它作上述三种运算恰能产生

The conclusion was proved that any subset in topological space brought thrity-four sets at most by doing the operations of complement?closure and boundary and a subset in real space was found,which just brought thrity-four different sets by doing three operations above-mentioned.