Sums of Boolean spaces represent every group

Jiří Adámek, V. Koubek, Vĕra Trnkov\'{a}
1975 Pacific Journal of Mathematics  
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.
doi:10.2140/pjm.1975.61.1 fatcat:dpqza44xovcn5mg37u5meadpti