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We introduce the inverse topology on the set of all minimal prime ideals of an MV-algebra $A$ and show that the set of all minimal prime ideals of $A$, namely $\mathrm{Min}\left(A\right)$, with the inverse topology is a compact space, Hausdorff, $T_0$-space and $T_1$-space. Furthermore, we prove that the spectral topology on $\mathrm{Min}\left(A\right)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on $\mathrm{Min}\left(A\right)$ is finer than the inverse topology on $\mathrm{Min}\left(A\right)$. Finally, by open sets of the inverse topology, we define and study a congruence relation...