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Inverse topology in MV-algebras

Fereshteh Forouzesh; Farhad Sajadian; Mahta Bedrood — 2019

Mathematica Bohemica

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 $Min (A)$ , with the inverse topology is a compact space, Hausdorff, $T_{0}$ -space and $T_{1}$ -space. Furthermore, we prove that the spectral topology on $Min (A)$ is a zero-dimensional Hausdorff topology and show that the spectral topology on $Min (A)$ is finer than the inverse topology on $Min (A)$ . Finally, by open sets of the inverse topology, we define and study a congruence relation...

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