Inverse topology in BL-algebras

Abstract

In this paper, we introduce Inverse topology in a BL-algebra A and prove the set of all minimal prime filters of A, namely Min(A) with the Inverse topology is a compact space, Hausdorff, T0 and T1-Space. Then, we show that Zariski topology on Min(A) is finer than the Inverse topology on Min(A). Then, we investigate what conditions may result in the equivalence of these two topologies. Finally, we define min-extension in BL-algebra and show that the mapping on Min(A) with respect to both the Zariski and the Inverse topology is continuous../files/site1/files/64/13.pdf

Keywords

• minimal prime filter
• zariski topology
• inverse topology
• min-extension.