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 PompeiuHausdor 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. Fix a topological space G. By T(G) denote the family of all single-valued continuous mappings of G into G. Relatively to the operation of composition, the set T(G) is a monoid (a semigroup with unity). A single-valued ' : G -! Com(Rn) is called a set-valued function on G. For any two set-valued functions ';   : G -! B(R) and t 2 R are determined the distance (';  ) = supfdP ('(x);  (x)) : x 2 Gg and the set-valued functions ' +  , '
  , -', ' [  , where (' [  )(x) = ('(x) [  (x), and t'. We put ('  f)(x) = '(f(x)) for all f 2 T(G), ' 2 SF(G) and x 2 G. Let SF(G;Rn) be the space of all set-valued functions on G with the metric . The space SF(G;Rn) is a complete metric space. A set-valued function   : G -! Rn is called lower (upper) semicontinuous if the set  -1(H) = fx 2 G :  (x) \ H 6= ;g is an open (a closed) subset of G for any open (closed) subset H of the space Rn. Denote by LSC(G;Rn) the family of all lower semicontinuous functions and by USC(G;Rn) the family of all upper semicontinuous functions on the space G. If ' 2 SF(G) and f 2 T(G), then 'f = '  f and 'f (x) = '(f(x)) for any x 2 G). Evidently, 'f 2 SF(G).