Set-Valued Almost Periodic Functions and Perfect Mappings

Abstract

Fix a natural number n ≥ 1. Denote by d the Euclidean distance on the n-dimensional Euclidian space Rn and by Com(Rn) the space of all non-empty compact subsets of Rn with the Pompeiu-Hausdorff distance dP(A, B). The space R = R1 is the space of reals and C = R2 is the space of complex numbers. The space (Com(Rn), dP) is a complete metric space.