Strongly zero-dimensional locales
The authors introduce a new definition of strongly zero-dimensional locales. Their conception is different from Johnstone's and almost all topological properties for strongly zero-dimensional spaces have a pointless localic form. Some properties and characterizations: (1) A topological space \(X\) is strongly zero-dimensional iff the lattice \(O(X)\) of open sets is strongly zero-dimensional. (2) A strongly zero-dimensional locale is zero-dimensional. A zero-dimensional Lindelöf locale is a strongly zero-dimensional locale. (3) For a compact locale, strong zero-dimensionality, zero-dimensionality and strong zero-dimensionality in Johnstone's sense are equivalent to each other. (4) The Stone-Čech compactification of a strongly zero-dimensional locale is strongly zero-dimensional.
scientific article; zbMATH DE number 1757445