Definition:Topological Closed Embedding

Definition

Let $X$ and $Y$ be topological spaces.

Let $f : X \to Y$ be a mapping.

Then $f$ is a (topological) closed embedding if and only if:

• $f$ is a topological embedding
• its image $f(X)$ is closed in $Y$

Also known as

A (topological) closed embedding is also known as a (topological) closed immersion.

Also see

• Definition:Topological Open Embedding