inclusion mapping (original) (raw)

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 combination of the symbols ⊂ and →. In the above definition, we have not used this convention. However, examples of this convention would be:

• •
  Let ι:X↪Y be the inclusion map from X to Y.
• •
  We have the inclusion Sn↪ℝn+1.