Extension
From Maths
(Unknown grade)
This page requires references, it is on a todo 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, [ilmath]f:X\rightarrow Y[/ilmath] is a new function, say [ilmath]\bar{f}:A\rightarrow B[/ilmath] where:
 [ilmath]X\subseteq A[/ilmath] and [ilmath]Y\subseteq B[/ilmath] such that:
 [ilmath]\bar{f}\vert_{X}=f[/ilmath], or symbolically:
 [ilmath]\forall x\in X[\bar{f}(x)=f(x)][/ilmath]
In words:
 The restriction of [ilmath]\bar{f} [/ilmath] to [ilmath]X[/ilmath] agrees with [ilmath]f[/ilmath]
Todo
TODO: These things
 Link with "induced" terminology.
References
