Discussion on the Topological Space on the Real Number Field

In the real line,the zero topological space and the joint topological space were constructed.For {Br(z,d)|r0,r∈Q,z∈R} was a basis to the zero topological space,it satisfied the second countability axiom.In the separating aspect.Space E is a normal space and regular space,which is also a Hausdorff space and T1 space,but it is not connected.The zero topological space is a T0 space,but it is not a T1 space.It is connective.