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.
@article{118501,
author = {Lutz Heindorf},
title = {Zero-dimensional Dugundji spaces admit profinite lattice structures},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {33},
year = {1992},
pages = {329-334},
zbl = {0789.54011},
mrnumber = {1189664},
language = {en},
url = {http://dml.mathdoc.fr/item/118501}
}
Heindorf, Lutz. Zero-dimensional Dugundji spaces admit profinite lattice structures. Commentationes Mathematicae Universitatis Carolinae, Tome 33 (1992) pp. 329-334. http://gdmltest.u-ga.fr/item/118501/
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