In this thesis , we present an expanded account of some spaces of vector-valued contiuous functions C(X,E) and C(Y,F) on locally compact spaces X and Y.We first define a support point and show that if T from C(X,E) into C(Y,F) be a map, then for each y in Y there exist a unique support point in X. Next we introduce and study disjoint preserving linear maps from C( X,E)into C(Y,F) is said to be separating or disjointness if fg=0 implise TfTg=0 for all f,g in C(X,E).The map from Y into sending each point of Y into its support point will denote by h.Then show that if T from C(X,E) into C(Y,F) is an injective separating map, Then the rang of h is dense i and h is continuous.Also we prove that if T and the invers of T is separating map, then X and Y are homeomorphic and if E is finite dimensional, then E=F. If X and Y be a compact Hausdorff space, E and F be a banach spaces and C(X,E) and C(Y,F) of continuous E-valued and F-valued functions, then Ix for each x in X defined Ix is f in C(X,E) such that f vanishes in a neighborhood of x. We show that if T from C(X,E) into C(Y,F) and the invers of T be a separating linear bijection, then for each x in X, there is a uniqe y in Y such that TIx=Iy.Also X and Y are homeomorphic. In this thesis we define weighted composition operator and prove that every biseparating linear T from C(X,E) into C(Y,F) is weighted composition operator.