Define an equivalence relation in , by declaring if and only if . Describe the quotient space and show that it is not a Hausdorff space.

My solution:

Let be the projection map. The equivalence class of , where , is since .

If then . Then the equivalence class of , where , is .

Thus the set is the union of and for all .

Can someone help me show that this space is not a Hausdorff space? Thanks