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 |
---|---|
Canonical name | TopologicalEmbedding |
Date of creation | 2013-03-22 15:30:59 |
Last modified on | 2013-03-22 15:30:59 |
Owner | kompik (10588) |
Last modified by | kompik (10588) |
Numerical id | 8 |
Author | kompik (10588) |
Entry type | Definition |
Classification | msc 54C25 |
Classification | msc 52B05 |
Synonym | imbedding |
Related topic | SubspaceTopology |