Algebraic subgroup lattices of topological groups

Scheiderer, Claus

Algebraic subgroup lattices of topological groups

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Datum

1986

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Algebra Universalis. 1986, 22(2-3), pp. 235-243. ISSN 0002-5240. eISSN 1420-8911. Available under: doi: 10.1007/BF01224029

Zusammenfassung

It is shown that the lattice of all closed subgroups of a compact topological group and the lattice of all connected closed subgroups of a pro-Lie group are algebraic, even arithmetic, if they are equipped with the order opposite to the natural one. The compact elements form ideals in these lattices and are explicitly determined. In the course of the proof the question is treated whether forming lattices of closed subgroups of topological groups commutes with projective limits.

Fachgebiet (DDC)

510 Mathematik

Zitieren

ISO 690

SCHEIDERER, Claus, 1986. Algebraic subgroup lattices of topological groups. In: Algebra Universalis. 1986, 22(2-3), pp. 235-243. ISSN 0002-5240. eISSN 1420-8911. Available under: doi: 10.1007/BF01224029

BibTex

@article{Scheiderer1986Algeb-23337,
  year={1986},
  doi={10.1007/BF01224029},
  title={Algebraic subgroup lattices of topological groups},
  number={2-3},
  volume={22},
  issn={0002-5240},
  journal={Algebra Universalis},
  pages={235--243},
  author={Scheiderer, Claus}
}

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