Give an exmple of a surjective function g from X onto [0,1] such that the quotient topology on [0,1] induced by g is not Hausdorff.
Thanks for any help.
What have you tried? Note that since is compact Hausdorff that saying the the topology induced on by some quotient map is equivalent to stating that is a closed map. So, find a quotient map which isn't closed and the resulting coinduced topology on will be non-Hausdorff.