Difference between revisions of "Extension"
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Latest revision as of 20:02, 8 April 2016
(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, [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]
To-do
TODO: These things
- Link with "induced" terminology.
References
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