Affiliations: [a] Faculty of Science, Xi’an Aeronautical University, Xi’an, China
| [b] School of Mathematics, Northwest University, Xi’an, China
| [c] Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Correspondence:
[*]
Corresponding author. Jiang Yang, School of Mathematics, Northwest University, Xi’an 710127, P.R. China. E-mail: yangjiang@stumail.nwu.edu.cn.
Abstract: In this paper, using a special family of extreme fuzzy filters
F
on a BL-algebra L, we construct a uniform structure
(L,K)
, and then the part
K
induce a uniform topology
TF
in L. Also, we prove that the pair
(L,TF)
is a topological BL-algebra, and some properties of
(L,TF)
are investigated. In particular, we show that
(L,TF)
is a first-countable, zero-dimensional, disconnected and completely regular space. At the same time, we give some characterizations of topological properties of
(L,TF)
, for example,
(L,TF)
is a discrete space if and only if g1 = {1}, and
(L,TF)
is a Hausdorff space if and only if g1 = {1}, where
g=∩F
. Finally, we naturally contact the relationship between isomorphism (algebraic invariant) and homeomorphism (topological invariant) in topological BL-algebras.
