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.

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