Just wondering if this is possible via mathematical conversion. I thought some Kernels might do this in the kernel space.

I got curious whether it's possible to create a general method that mathematically converts any collection of extrapolation points given some data into an interpolation points in the transformed space.

Mathematically speaking:

Does there always exist some function $f:X \rightarrow Y$ such that $f(A) \subset f(U)$ holds for any set of exterior points $A \subset X$ of some set of interpolation region $U \subset X$, $U \cap A = \emptyset $. If not, under which conditions would that hold?


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