### A priori estimates for the existence of a solution for a multi-point boundary value problem.

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For a discrete dynamical system given by a compact Hausdorff space X and a continuous selfmap f of X the connection between minimality, invertibility and openness of f is investigated. It is shown that any minimal map is feebly open, i.e., sends open sets to sets with nonempty interiors (and if it is open then it is a homeomorphism). Further, it is shown that if f is minimal and A ⊆ X then both f(A) and ${f}^{-1}\left(A\right)$ share with A those topological properties which describe how large a set is. Using these results...

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