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

  • Authors:

  • Xiao-Fei Yang;Sheng-Gang Li

  • Affiliations:

  • College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China and School of Science, Xi'an Polytechnic University, Xi'an 710048, PR China;College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, PR China

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2013

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Abstract

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.