One question I've had lately in my independent study of topology is the problem of how to show two sets are homeomorphic to each other. I am not sure how I would go about doing this in a general, or even specific case. One problem that wants me to demonstrate this is in Mendelson: Prove that an open interval (a,b) considered as a subspace of the real line is homeomorphic to the real line. Now, I know that a homeomorphism is a map where both it and its inverse are continuous, so I'm wondering if all that is needed to show two sets are homeomorphic is to simply define a mapping between the two. However, I don't know if this is right. Can someone please clarify? Thanks.