Completion of stratified (L,M)-filter tower spaces

The notion of stratified (L,M)-filter tower spaces is introduced and the resulting category is shown to be a strong topological universe. Completions of stratified (L,M)-filter tower spaces are considered and a sufficient and necessary condition for a stratified (L,M)-filter tower space to have a completion is also given. It is proved that the reflective modification of completion for a stratified (L,M)-Cauchy tower space, considered as a stratified (L,M)-filter tower space, is still a completion for this stratified (L,M)-Cauchy tower space.