inclusion mapping
Definition Let $X$ be a subset of $Y$. Then the inclusion map^{} from $X$ to $Y$ is the mapping
$\iota :X$  $\to $  $Y$  
$x$  $\mapsto $  $x.$ 
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 $\hookrightarrow $ instead of $\to $ when defining or mentioning an inclusion map. This hooked arrow symbol $\hookrightarrow $ can be seen as combination^{} of the symbols $\subset $ and $\to $. In the above definition, we have not used this convention. However, examples of this convention would be:

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Let $\iota :X\hookrightarrow Y$ be the inclusion map from $X$ to $Y$.

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We have the inclusion ${S}^{n}\hookrightarrow {\mathbb{R}}^{n+1}$.
Title  inclusion mapping 

Canonical name  InclusionMapping 
Date of creation  20130322 13:43:08 
Last modified on  20130322 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 