Extension

(Unknown grade)

This page requires references, it is on a to-do list for being expanded with them.

Please note that this does not mean the content is unreliable, it just means that the author of the page doesn't have a book to hand, or remember the book to find it, which would have been a suitable reference.

Definition

An extension of a mapping, $f:X\rightarrow Y$ is a new function, say $\bar{f}:A\rightarrow B$ where:

• $X\subseteq A$ and $Y\subseteq B$ such that:
• $\bar{f}\vert_{X}=f$, or symbolically:
  • $\forall x\in X[\bar{f}(x)=f(x)]$

In words:

• The restriction of $\bar{f}$ to $X$ agrees with $f$

To-do

---

TODO: These things

---

• Link with "induced" terminology.