I am looking for examples of Hausdorff spaces. I think that the set of rationals is an example of a Hausdorff space or the Cantor set.

I am also needing an example of two spaces that are homeomorphic to each other and indeed share the Hausdorff property. I was thinking that the Cantor set would be a good example for this, but not sure if I am thinking correctly.

Any help would be great.