TY - JOUR
ID - 3256
TI - A COMMON FRAMEWORK FOR LATTICE-VALUED, PROBABILISTIC AND APPROACH UNIFORM (CONVERGENCE) SPACES
JO - Iranian Journal of Fuzzy Systems
JA - IJFS
LA - en
SN - 1735-0654
AU - Jager, Gunther
AD - School of Mechanical Engineering, University of Applied Sciences
Stralsund, 18435 Stralsund, Germany
Y1 - 2017
PY - 2017
VL - 14
IS - 3
SP - 67
EP - 81
KW - Stratified lattice-valued uniformity
KW - Stratified lattice-valued uniform convergence space
KW - Probabilistic uniform convergence space
KW - Approach uniform convergence space
KW - Stratified $LM$-filter
DO - 10.22111/ijfs.2017.3256
N2 - 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.
UR - https://ijfs.usb.ac.ir/article_3256.html
L1 - https://ijfs.usb.ac.ir/article_3256_cfb014316ad07007c6f93e1601624252.pdf
ER -