article · Pacific Journal of Mathematics · 1975

Sums of Boolean spaces represent every group

Jiřı́ Adámek, Vácłav Koubek, Věra Trnková

Cited by 46Open access

Abstract

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.

Cite this paper

APA 7

Adámek, J., Koubek, V., & Trnková, V. (1975). Sums of Boolean spaces represent every group. Pacific Journal of Mathematics, 61(1), 1–6. https://doi.org/10.2140/pjm.1975.61.1

MLA 9

Adámek, Jiřı́, et al. “Sums of Boolean spaces represent every group.” Pacific Journal of Mathematics, vol. 61, no. 1, 1975, pp. 1–6, https://doi.org/10.2140/pjm.1975.61.1.

Chicago

Adámek, Jiřı́, Vácłav Koubek, and Věra Trnková. 1975. “Sums of Boolean spaces represent every group.” Pacific Journal of Mathematics 61 (1): 1–6. https://doi.org/10.2140/pjm.1975.61.1.

Harvard

Adámek, J., Koubek, V. and Trnková, V. (1975) ‘Sums of Boolean spaces represent every group’, Pacific Journal of Mathematics, 61(1), pp. 1–6. Available at: https://doi.org/10.2140/pjm.1975.61.1.

BibTeX

@article{adamek1975sums,
  title = {{Sums of Boolean spaces represent every group}},
  author = {Adámek, Jiřı́ and Koubek, Vácłav and Trnková, Věra},
  journal = {Pacific Journal of Mathematics},
  volume = {61},
  number = {1},
  pages = {1--6},
  year = {1975},
  doi = {10.2140/pjm.1975.61.1}
}

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