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If H is a homeomorphism from $R^{n}$ to itself, and P is a compact polyhedron, is H(P) piecewise-linear homeomorphic to P?
I know that, in a manifold of dimension $\geq$ 5,there can exist polyhedra P and Q that are homeomorphic but not piecewise-linear homeomorphic. Can this happen if P and Q are
compact subsets of $R^{n}$ and the homeomorphism maps $R^{n}$ to itself?
