De Vries algebras and compact regular frames
It is proved that the category of de Vries algebras is equivalent to the category of compact regular frames. Alhough this result can be deduced from the existing literature, the proof would go via employing the category of compact Hausdorff spaces and depends on the axiom of choice. In this paper a new proof is proposed which is direct and avoids usage of the axiom of choice. It is also proved that the category of completely regular de Vries algebras is equivalent to the category of compact completely regular frames. Other results are that the category of zero-dimensional de Vries algebras is equivalent to the category of zero-dimensional compact frames; and that the category of extremally disconnected de Vries algebras is equivalent to the category of extremally disconnected compact regular frames.
scientific article; zbMATH DE number 6121296
scientific article