Definition:Inclusion Mapping

Definition
The inclusion mapping $$i_S: S \to T$$ is a mapping on a set $$S$$ defined when $$S \subseteq T$$:
 * $$i_S: S \to T: \forall x \in S: i_S \left({x}\right) = x$$

It can be seen that the inclusion mapping i_S is the restriction to $$S$$ of the identity mapping $$I_T: T \to T$$.

Notation
Beware the notation used. Always be sure you understand what is being used.

Some authors use $$i_S$$ (or similar) for the identity mapping, and so use something else, probably $$\iota_S$$ (Greek "iota"), for the inclusion mapping.