# Actual embedding

In mathematics , the **actual embedding is** an embedding term that is mainly used in topology when examining manifolds with a boundary .

## definition

Be and manifolds with boundaries .

An image is called *actual embedding* if it

- is an embedding, and
- such as

applies.

The definition is equivalent to the fact that the restriction is to an embedding and an actual mapping .

In the theory of differentiable manifolds one also demands that it is transversal to .

## literature

- Hempel, John 3-manifolds. Reprint of the 1976 original. AMS Chelsea Publishing, Providence, RI, 2004. ISBN 0-8218-3695-1