%0 Journal Article
%T A COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES
%J Iranian Journal of Fuzzy Systems
%I University of Sistan and Baluchestan
%Z 1735-0654
%A Jager, Gunther
%D 2017
%\ 06/29/2017
%V 14
%N 3
%P 67-81
%! A COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES
%K Stratified lattice-valued uniformity
%K Stratified lattice-valued uniform convergence space
%K Probabilistic uniform convergence space
%K Approach uniform convergence space
%K Stratified $LM$-filter
%R 10.22111/ijfs.2017.3256
%X We develop a general framework for various lattice-valued, probabilistic and approach uniform convergence spaces. To this end, we use the concept of $s$-stratified $LM$-filter, where $L$ and $M$ are suitable frames. A stratified $LMN$-uniform convergence tower is then a family of structures indexed by a quantale $N$. For different choices of $L,M$ and $N$ we obtain the lattice-valued, probabilistic and approach uniform convergence spaces as examples. We show that the resulting category $sLMN$-$UCTS$ is topological, well-fibred and Cartesian closed. We furthermore define stratified $LMN$-uniform tower spaces and show that the category of these spaces is isomorphic to the subcategory of stratified $LMN$-principal uniform convergence tower spaces. Finally we study the underlying stratified $LMN$-convergence tower spaces.
%U https://ijfs.usb.ac.ir/article_3256_cfb014316ad07007c6f93e1601624252.pdf