inclusion mapping

Definition Let X be a subset of Y. Then the inclusion mapMathworldPlanetmath from X to Y is the mapping

ι:X Y
x x.

In other words, the inclusion map is simply a fancy way to say that every element in X is also an element in Y.

To indicate that a mapping is an inclusion mapping, one usually writes instead of when defining or mentioning an inclusion map. This hooked arrow symbol can be seen as combinationMathworldPlanetmathPlanetmath of the symbols and . In the above definition, we have not used this convention. However, examples of this convention would be:

  • Let ι:XY be the inclusion map from X to Y.

  • We have the inclusion Snn+1.

Title inclusion mapping
Canonical name InclusionMapping
Date of creation 2013-03-22 13:43:08
Last modified on 2013-03-22 13:43:08
Owner Koro (127)
Last modified by Koro (127)
Numerical id 9
Author Koro (127)
Entry type Definition
Classification msc 03E20
Synonym inclusion map
Synonym inclusion
Related topic Pullback2