Geodesic
Spectra of compact regular frames
Theory and applications of categories, Tome 31 (2016), pp. 365-383

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By Isbell duality, each compact regular frame L is isomorphic to the frame of opens of a compact Hausdorff space X. In this note we study the spectrum Spec(L) of prime filters of a compact regular frame L. We prove that X is realized as the minimum of Spec(L) and the Gleason cover of X as the maximum of Spec(L). We also characterize zero-dimensional, extremally disconnected, and scattered compact regular frames by means of Spec(L).

Publié le :
Classification : 06D22, 06D20, 06E15, 54G05, 54G12
Keywords: Frame, the spectrum of a frame, compact regular frame, compact Hausdorff space, Gleason cover, zero-dimensional frame, extremally disconnected frame, scattered frame 
@article{TAC_2016_31_a11,
     author = {Guram Bezhanishvili and David Gabelaia and Mamuka Jibladze},
     title = {Spectra of compact regular frames},
     journal = {Theory and applications of categories},
     pages = {365--383},
     publisher = {mathdoc},
     volume = {31},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2016_31_a11/}
}
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Guram Bezhanishvili; David Gabelaia; Mamuka Jibladze. Spectra of compact regular frames. Theory and applications of categories, Tome 31 (2016), pp. 365-383. http://geodesic.mathdoc.fr/item/TAC_2016_31_a11/