Hello. I study topology nowadays. But I have a difficult in topology. Could you help me?

This is the problem.

Let (R,U)=usual topology & A:subset of R & B=R-A.
Let function fR,U)→B∪{0}, f(x)=0(x∈A), f(x)=x(x∈B).
Let T: quotient topology of f.

Find A such that 1.quotient space (B∪{0},T):T2 ,2. (0,1)∪(1,2)⊂A⊂[0,2]∪{4}.


Thank you.