Definition:Embedding (Topology)

Definition
Let $A, B$ be topological spaces.

Let $f: A \to B$ be a mapping.

Let the restriction $f {\restriction_{A \times f \left({A}\right)}}$ of $f$, with its be a homeomorphism.

That is, let $f$ be a continuous, open injection.

Then $f$ is an embedding of $A$ into $B$.

Also known as
Some authors use the terms topological embedding, imbedding, or topological imbedding.

Also defined as
Some authors define an embedding as a continuous injection.

However, it is generally accepted that such a mapping is required to be open as well, in order for this definition to hold.

Also see

 * Continuous Injection from Compact Space to Hausdorff Space is Embedding