Question: Let K be a compact subset of a normed linear space X. For every > 0, there exists a finite-dimensional convex set S

Let K be a compact subset of a normed linear space X. For every ε > 0, there exists a finite-dimensional convex set S ⊆ X and a continuous function h: K → S such that S⊆ conv K and
||h(x) - x|| < ε for every x ∊ K

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