Embedding

Definition (Embedding)

An embedding of $(X,{\tau }_X)$ in $(Y,{\tau }_Y)$ is a map from $f:X\to Y$ which carries $X$ homeomorphically to its image.

For example, imagine mapping our $S^1$ circle to a trefoil knot in ${\mathbb{R}}^3$. This however, is not a homeomorphism.