In topology, what is the difference between a homeomorphism and an embedding?

Answer 1

An embedding is an injective continuous map, which is a homeomorphism onto its image. An embedding does not have to be surjective.

In other words:

f : X -> Y is an embedding
if and only if
f is continuous and injective, and the range-restricted map
g : X -> f(X) (where g(x)=f(x) for all x in X) is a homeomorphism.

Answer 2

a homeomorphism is like the name says a mapping from a curve ont another curve. The first curve can have the same form as the second one via a continous mapping.
An embedding has nothing to do with formpreserving properties.