A representation of CD omega(K)-spaces

We give a representation of the space CDw(K) which was defined by Abramovich and Wickstead. We apply this to reprove the Banach-Stone type theorem for CDw(K) spaces. By using this representations we note that for each compact Hausdorff space K without isolated points there exists compact Hausdorff space T which contains K as a closed subspace such that the Dedekind completion of C(T) is B(K)