topological embedding

Let X, Y be topological spacesMathworldPlanetmath. A map f:XY is said to be an embeddingMathworldPlanetmathPlanetmath (or imbedding) if the restrictionPlanetmathPlanetmathPlanetmath f:Xf[X] is homeomorphismPlanetmathPlanetmath.

The notation f:XY is often used for embeddings.

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


  • 1 Wikipedia’s entry on
  • 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