# nonhausdorff

1. ### Example of a non-Hausdorff surjective function

Let X = [-1,1] and give X the usual topology. 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.
2. ### Quotient map from Hausdorff to non-Hausdorff space

Does a quotient map p : X to Y where X is Hausdorff and Y is not exist?
3. ### Non-Hausdorff Quotient Space

This is a homework problem I've been struggling with, so I'd prefer a gentle nudge rather than the absolute solution. Consider a topological space X that is the disjoint union of two real lines. ie. X = R + R. Define the equivalence relation ~ : (a,0) ~ (b,1) iff a = b, but neither equal to...