Extension

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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

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TODO: These things

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• Link with "induced" terminology.