Kybernetika

In this paper we introduce stable topology and F-topology on the set of all prime filters of a BL-algebra A and show that the set of all prime filters of A, namely Spec(A) with the stable topology is a compact space but not T₀. Then by means of stable topology, we define and study pure filters of a BL-algebra A and obtain a one to one correspondence between pure filters of A and closed subsets of Max(A), the set of all maximal filters of A, as a subspace of Spec(A). We also show that for any filter F of BL-algebra A if σ(F)=F then U(F) is stable and F is a pure filter of A, where σ(F)= { a\in A | y\wedge z=0 for some z\in F and y \in a^\perp } and U(F) = { P \in Spec(A) \vert F \nsubseteq P }.