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Sums of Boolean spaces represent every group
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