Extreme fuzzy filters and its application on BL-algebras

摘要

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 T-F in L. Also, we prove that the pair (L, T-F) is a topological BL-algebra, and some properties of (L, T-F) are investigated. In particular, we show that (L, T-F) is a first-countable, zero-dimensional, disconnected and completely regular space. At the same time, we give some characterizations of topological properties of (L, T-F), for example, (L, T-F) is a discrete space if and only if g(1) = {1}, and (L, T-F) is a Hausdorff space if and only if g(1) = {1}, where g = boolean AND F. Finally, we naturally contact the relationship between isomorphism (algebraic invariant) and homeomorphism (topological invariant) in topological BL-algebras.