Abstract
We prove that the topology of a compact Hausdorff topological Heyting algebra is a Stone topology. It then follows from known results that a Heyting algebra is profinite iff it admits a compact Hausdorff topology that makes it a compact Hausdorff topological Heyting algebra.
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Bezhanishvili, G., Harding, J. Compact Hausdorff Heyting algebras. Algebra Univers. 76, 301–304 (2016). https://doi.org/10.1007/s00012-016-0387-y
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DOI: https://doi.org/10.1007/s00012-016-0387-y