Sums of Boolean spaces represent every group
Jiřı́ Adámek, Vácłav Koubek, Vĕra Trnkov\'{a} · Pacific Journal of Mathematics · 1975
For every Abelian group (S, +) there exist Boolean -i.e., compact, O-dimensional -topological spaces X s , se S f such that s + t = u if and only if X u is homeomorphic to the disjoint union of X, and X t .The method of the proof of this theorem is topological, utilizing mostly properties of Cech-Stone compactifications of various spaces.A corollary, obtained from well-known dualities, is the representability of Abelian groups (in an analogous sense) by products of rings, lattices, Boolean algebras, Banach spaces or Banach algebras.