@article {
author = {Jager, Gunther},
title = {A COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES},
journal = {Iranian Journal of Fuzzy Systems},
volume = {14},
number = {3},
pages = {67-81},
year = {2017},
publisher = {University of Sistan and Baluchestan},
issn = {1735-0654},
eissn = {2676-4334},
doi = {10.22111/ijfs.2017.3256},
abstract = {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.},
keywords = {Stratified lattice-valued uniformity,Stratified lattice-valued uniform convergence space,Probabilistic uniform convergence space,Approach uniform convergence space,Stratified $LM$-filter},
url = {https://ijfs.usb.ac.ir/article_3256.html},
eprint = {https://ijfs.usb.ac.ir/article_3256_cfb014316ad07007c6f93e1601624252.pdf}
}