# topological embedding

Let $X$, $Y$ be topological spaces. A map $f:X\to Y$ is said to be an embedding (or imbedding) if the restriction $f:X\to f[X]$ is homeomorphism.

The notation $f:X\hookrightarrow Y$ is often used for embeddings.

The embeddings correspond to the subspaces. Observe that $f$ and the inclusion map of the subspace $f[X]$ into $X$ differ only up to a homeomorphism.

## References

• 1 Wikipedia’s entry on http://en.wikipedia.org/wiki/embeddingEmbedding
• 2 S. Willard, General topology, Addison-Wesley, Massachussets, 1970.
Title topological embedding TopologicalEmbedding 2013-03-22 15:30:59 2013-03-22 15:30:59 kompik (10588) kompik (10588) 8 kompik (10588) Definition msc 54C25 msc 52B05 imbedding SubspaceTopology