Strongly retractive Boolean algebras
Boolean semigroup rings and exponentials of compact zero-dimensional spaces
Zero-dimensional Dugundji spaces admit profinite lattice structures
We prove what the title says. It then follows that zero-dimensional Dugundji space are supercompact. Moreover, their Boolean algebras of clopen subsets turn out to be semigroup algebras.
Another note on countable Boolean algebras
We prove that a Boolean algebra is countable iff its subalgebra lattice admits a continuous complementation.
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