2026/06/07 by G. Bezhanishvili, P. Bhattacharjee, S. D. Melzer +1 · 1 voice
Mathematics · #math.GN
It is an interesting open problem whether every compact Hausdorff space can be realized as the maximal d-spectrum of an arithmetic frame. We approach this problem by generalizing the d-nucleus to a stably continuous frame. We use Priestley duality to characterize the resulting \underline d-nucleus, which allows us to prove that every locally compact Hausdorff space can be realized as the maximal \underline d-spectrum of a continuous regular frame. As a corollary, we obtain that every locally Stone space can be realized as the maximal d-spectrum of an algebraic regular frame.