Solving a recently raised problem, we prove that if f maps continuously a compact subset X of Rn into Rn, and all fibers of points in f (∂X) have diameter smaller than the distance of a point of X from the boundary of X, then this point is mapped by f in the interior of f (X).
On the domain invariance theorem
DE MARCO, GIUSEPPE
2004
Abstract
Solving a recently raised problem, we prove that if f maps continuously a compact subset X of Rn into Rn, and all fibers of points in f (∂X) have diameter smaller than the distance of a point of X from the boundary of X, then this point is mapped by f in the interior of f (X).
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