Observing that each Tychonoff space X has the minimal basically disconnected cover (ΛX, Λ$sub$X/) and the .realcompact-ification $upsilon$X, we introduce a concept of stable $sigma$Z(X)#-ultrafilters and give internal characterizations of Tychonoff spaces X for which Λ($upsilon$X) : $upsilon$(ΛX).