Stratified L-ordered quasiuniform limit spaces

Abstract

By making use of the intrinsic lattice-valued inclusion orders of L-subsets and that of stratified L-filters, a concept of stratified L-ordered quasiuniform limit structure is proposed, which is asymmetric and available to establish a framework of asymmetric structures. Then the category of stratified L-ordered quasiuniform limit spaces is introduced and its categorical properties are shown. The next objective of the paper is to propose a concept of stratified L-ordered principle quasiuniform limit space, and we prove that the category of stratified L-quasiuniform spaces can be embedded into the category of stratified L-quasiuniform limit spaces as a bireflective subcategory. Moreover, two ways of inducing stratified L-ordered limit structures from stratified L-ordered quasiuniform structures are presented, and the method of obtaining stratified [0,1]-ordered quasiuniform structures from [0,1]-ordered probabilistic quasiuniform limit structures and fuzzy quasi-metrics is introduced in the paper.