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Given a map, [ilmath]f:X\rightarrow Y[/ilmath] for sets, [ilmath]X[/ilmath] and [ilmath]Y[/ilmath], and given any [ilmath]A\in\mathcal{P}(X)[/ilmath][Note 1] (so [ilmath]A\subseteq X[/ilmath] - and is any subset) we define a new function, the restriction of [ilmath]f[/ilmath] to [ilmath]A[/ilmath] as:

  • [ilmath]f\vert_A:A\rightarrow Y[/ilmath] by [ilmath]f\vert_A:a\mapsto f(a)[/ilmath]


TODO: These

  1. Link with inclusion mapping


  1. Recall [ilmath]\mathcal{P}(X)[/ilmath] denotes the power-set of [ilmath]X[/ilmath]