By means of a characterization of compact spaces in terms of open C_D^*-filters induced by a , a - and open C_D^*-filters process of compactifications of an arbitrary topological space Y is obtained in Sec. 3 by embedding Y as a dense subspace of , Y_S = {ε |ε is an open C_D^*-filter that does not converge in Y}, Y_T = {A|A is a basic open C_D^*-filter that does not converge in Y}, is the topology induced by the base B = {U*|U is open in Y, U ≠φ} and U* = {F∈Y_s^w (or Y_T^w)|U∈F}. Furthermore, an arbitrary Hausdorff compactification (Z, h) of a Tychonoff space X can be obtained from a by the similar process in Sec.3.