The Fixed-Point Property Under Induced Interval Maps of Continua

Аннотация

Let f : I → I be a continuous map of a compact interval I and let C(I) be hyperspace of all compact subintervals of I equipped with the Hausdorff metric. We study the fixed-point property of the subsets of C (I) with respect to any induced interval map ℱ : C (I) → C (I). In particular, we prove that any nonempty subcontinuum of C (I) possesses the fixed-point property.