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, T
0 and T
1-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.
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